Die capable of being opened, manufacturing method thereof, and mold

Information

  • Patent Grant
  • 6824725
  • Patent Number
    6,824,725
  • Date Filed
    Monday, October 28, 2002
    21 years ago
  • Date Issued
    Tuesday, November 30, 2004
    19 years ago
Abstract
In a die which has a regular polyhedron form and which can be opened into a continuous polygonal form on a plane, boundary areas (Rb) between planes (11 through 16) on the inner side of the regular polyhedron have inclination angles determined according to the regular polyhedron. In addition, engaging portions (21a, 21b, 24a, 24b, 25a, 25b, 26a, 26b) not exceeding the respective boundary areas (Rb) are placed on the boundary areas (Rb) of predetermined planes (11 through 16). Such a die is formed by injecting plastic resin within a mold (31, 32) according to the form of the opened die. This realizes a three-dimensional die capable of being opened onto a two-dimensional plane, which has only been fictionally conceived, and further provides a manufacturing method thereof.
Description




BACKGROUND OF THE INVENTION




The present invention relates to a die (dice) used with board games, and the manufacturing method thereof, and further relates to a mold used for manufacturing the die.




Various types of board games have long been enjoyed, such as shogi, go, dominoes, Othello, and so forth. Among such board games, there are many games wherein dice are cast, and the results the dice roll are reflected in the subsequent game, such as Parcheesi. In such board game using dice, the rolling results of the dice greatly affects winning or losing the game.




On the other hand, recently, there are comic books portraying a fictional entertainment world, which describe a fictional board game called Dragon Dice & Dungeons (hereafter abbreviated to “DDD”). In the DDD, characters battle with each other in the comics. The DDD is at first specified by using multiple dice having markings different from those of standard dice. Each die is effective to cause effects and rolling results of the dice. In addition, the DDD is also specified by opening each of the dice in a two-dimensional manner on the board. In the case of this DDD, opening the dice two-dimensionally determines routes and encampments according to the two-dimensional polygonal form of the opened dice. That is to say, with DDD, not only the rolling results of the dice are used in the game, but also the dice are also used for determining routes and encampments by the opened dice. Further, with a fictional world described by the comic, monsters appear from the opened die on the board according to individual dice and battle with the other monster or monsters virtually.




However, there are many problems in realizing such a fictional board game described in the comics as an actual board game. For example, in the event that the above-described DDD is to be played by actual players, dice which can be two-dimensionally opened, i.e., opened and closed, by the players, are necessary, but conventionally there has never been a proposal made of dice capable of being opened out or opened and closed, and what configuration would allow this to be realized cannot be guessed from the comics. Also, the material of a die capable of being opened, the die configuration necessary for opening, and so forth, cannot be guessed. Further, there are problems, such as placing monsters or the like within dice capable of being opened would make the dice too large, and further, the monsters in the dice would throw the center of gravity of the dice off-center and change the probability of what the cast dice show, so this is not realistic.




SUMMARY OF THE INVENTION




Accordingly, it is an object of the present invention to realize a fictional board game using dice which can be opened such as with DDD, as an actual board game.




It is another object of the present invention to realize a die which can be opened two-dimensionally by a player in a polygonal form.




It is a further object of the present invention to provide a manufacturing method for a die which can be opened two-dimensionally, and a mold used for the manufacturing thereof.




According to one aspect of this invention, there is provided a die which is structured by a polyhedron having multiple planes (


11


through


16


) of a similar shape and which is opened into a continuous polygonal area on a plane, wherein, in the assembled state of the polyhedron, the die has outer planes (


11




o


through


16




o


) positioned on the outer side and inner planes (


11




i


through


16




i


) positioned on the inner side, and has boundary areas (Rb) having a predetermined inclination angle at boundaries of the polygonal area of the inner side, while boundary areas (Rb) of predetermined planes of the opened polygonal area have engaging portions (


21




a


,


21




b


,


24




a


,


24




b


,


25




a


,


25




b


,


26




a


,


26




b


) of a size not exceeding each boundary area (Rb).




According to another aspect of this invention, there is provided a method for manufacturing a die which is configured of a polyhedron having multiple planes (


11


through


16


) of a similar shape and which can be opened into a continuous polygonal area on a plane, wherein a mold (


31


,


32


) is prepared, the mold (


31


,


32


) having the form of the opened polyhedron and comprising a portion equivalent to the opened polyhedron having a predetermined spacing in the thickness direction, and portions equivalent to boundaries (Rb) of the polyhedron having spacing narrower than the predetermined spacing, and wherein forming is performed by injecting a predetermined resin into the mold (


31


,


32


), thereby obtaining the die.




According to yet another aspect of this invention, there is provided a mold (


31


,


32


) for manufacturing a die which is configured of a polyhedron having multiple planes (


11


through


16


) each with mutually equal forms and which can be opened into a continuous polygonal area on a plane, the mold having the form of the opened polyhedron and comprising a portion equivalent to the opened polyhedron having a predetermined spacing in the thickness direction, and portions equivalent to boundaries (Rb) of the polyhedron having spacing narrower than the predetermined spacing.




According to yet another aspect of this invention, there is provided a die which can be opened in a polygonal configuration on a flat surface, which can be assembled three-dimensionally, and which is structured by a plurality of planes. When the die is three-dimensionally assembled, a gap is left between two of the planes, at least predetermined one of which is smaller in size than the remaining planes.











BRIEF DESCRIPTION OF THE DRAWINGS





FIG. 1

is a perspective view for describing a die according to one embodiment of the present invention;





FIGS. 2A

,


2


B, and


2


C are inner surface, edge, and outer surface drawings for describing the die shown in

FIG. 1

opened;





FIG. 3

is a partial cross-sectional view for describing the die shown in

FIGS. 2A through 2C

opened, in greater detail:





FIG. 4

is a diagram for describing the mold used for manufacturing the die according to the present invention;





FIG. 5

is a schematic configuration diagram for describing a die according to another embodiment of the present invention;





FIGS. 6A through 6F

are drawings for describing the die opened in two-dimensional forms different to the example shown in

FIGS. 2A through 2C

;





FIG. 7

is a perspective view for describing a die according to another embodiment of the present invention;





FIGS. 8A

,


8


B, and


8


C are inner surface, edge, and outer surface drawings for describing the die shown in

FIG. 1

opened;





FIG. 9

is a perspective view for describing a die according to yet another embodiment of the present invention;





FIG. 10

is a diagram illustrating an opened example of the die shown in

FIG. 9

; and





FIG. 11

is a diagram illustrating another opened example of the die shown in FIG.


9


.











DESCRIPTION OF PREFERRED EMBODIMENTS





FIG. 1

shows a perspective view illustrating the external view of a die relating to the present invention, comprising a cube, and markings different to those of standard dice are displayed on each of the six square planes making up the outer surface thereof. These marks each have crucial meanings in the game, but are irrelevant to the present invention, so description thereof will be omitted here.




The die shown in

FIG. 1

can be opened onto a two-dimensional polygonal plane as shown in

FIGS. 2A through 2C

, by pulling the plane upwards in an upward direction. Specifically, the die shown in

FIG. 1

is configured by linking six square planes (hereafter called first through sixth planes), and also providing engaging portions at boundaries positioned at the perimeter of certain planes. Further, the die shown in the figure is formed by injecting polypropylene resin in a mold and forming. In this example, polypropylene resin has been used, but other resin may be used instead. Here, an actual die has heightwise and widthwise dimensions of 22.88 mm each, and further is formed of first through sixth planes


11


through


16


each having thickness of 3 mm.





FIG. 2A

illustrates the inner surface which appears when the die according to a first embodiment of the present invention is opened two-dimensionally. The illustrated inner surface is positioned inside the die in the event that the die is assembled as shown in

FIG. 1

, and thus not visible from the outside.

FIG. 2B

is a diagram illustrating a side of one of the planes of the opened die, and

FIG. 2C

is a diagram illustrating the outer surface which is positioned outside the die in the event that the die is assembled, with the markings shown in

FIG. 1

displayed on each plane. Now,

FIGS. 2A through 2C

only illustrate one example of polygonal forms which can be opened from the die shown in

FIG. 1

, and it should be noted that the present invention may be configured so as to be opened into other polygonal forms.




The die according to the present invention will be described in further detail, with reference to

FIGS. 2A through 2C

. As shown in

FIG. 2A

, the inner surface of the die is configured of first through sixth square inner planes


11




i


through


16




i


, corresponding to the first through sixth planes


11


through


16


. In the example shown in the figure, the first through fourth inner planes


11




i


through


14




i


are linearly linked, and the second, fifth, and sixth inner planes


12




i


,


15




i


, and


16




i


, are also linearly linked. It can thus be clearly understood that the die according to the present invention can be opened into an area with a polygonal form of six continuous planes, without the planes being separated one from another. It is also clear from the figure that the inner planes


11




i


through


16




i


have a center area Rc which is of a flat and square form, and a boundary area Rb which surrounds the perimeter thereof.




In this example, the boundary or border areas Rb of the inner planes


11




i


through


16




i


each have a width of 2 mm, and have an inclination angle of around 45 degrees. On the other hand, the center areas of the inner planes


11




i


through


16




i


each have an area of 18 mm×18 mm, and have a thickness of 3 mm. Certain symbols are either printed on these center areas, or printed stickers are applied thereto.




Now, with the continuously-formed sixth and second planes


16


and


12


as an example, the boundary area Rb and bridge portion Br between the mutually adjacent planes will be described, with reference to FIG.


3


. As shown in the figure, boundary areas Rb having inclination angle portions of around 45 degrees are formed to the inner sixth and second inner side


16




i


and


12




i


sides of the sixth and second planes


16


and


12


, and the inclined portions are provided over a distance of 2 mm in the direction of the thickness. The planes


16


and


12


are linked by an extremely thin thin-film-like bridge portion Br provided at the edge portion of the inclined portions. Here, the bridge portion Br shown in the figure has a width of 0.6 mm, and a thickness of around 0.2 mm. Thus, the bridge portion Br liking adjacent planes is extremely thin in comparison with the adjacent planes, so a linearly extending groove is formed between the outer planes


16




o


and


12




o


of either plane, as shown in FIG.


3


.




Accordingly, the planes


16


and


12


can be bent inwards bordering on this groove portion. Also, the inclination angle of adjacent boundary areas Rb is around 45 degrees, so in the event that the adjacent planes


16


and


12


are bent inwards, bending of 90 degrees or more can be prevented.




Description will be made regarding the structure of the engaging portion for maintaining the form of the die when the die shown in

FIG. 1

is assembled, with reference to

FIGS. 2A and 2B

. At the boundary area Rb of the first inner plane


11




i


shown in

FIG. 2A

, a pair of recesses


21




a


and


21




b


are formed at the portion linking the sixth and second inner planes


16




i


and


12




i


within a range not crossing the boundary area Rb.




On the other hand, a protrusion


26




b


which engages the recess


21




b


formed to the boundary area Rb of the first inner plane


11




i


is provided to the boundary area Rb of the sixth inner plane


16




i


which is linked to the first inner plane


11




i


, and also, a protrusion


25




a


which engages the recess


21




b


formed to the boundary area Rb of the first inner plane


11




i


is provided to the boundary area Rb of the fifth inner plane


15




i.






Also, it is preferable that the protrusions provided on the boundary area Rb are formed so as to not protrude out upwards from the inner plane. This is because with the above-described DDD, the die opened on a flat plane is used as an encampment, and in the event that there is something protruding out upwards from the inner plane, the characters placed on the inner plane may become unstable, or the characters may hang thereon at the time of moving the characters and cause the position of the die to move, and this is to prevent such.




In the example shown in

FIGS. 2A through 2C

, at the time of assembling the die, protrusions


24




a


and


24




b


are formed at the boundary area Rb provided on the fourth inner plane


14




i


coming into contact with the fifth and sixth inner planes


15




i


and


16




i


, and recesses


25




b


and


26




a


are formed at the boundary areas Rb provided on the fifth and sixth inner planes


15




i


and


16




i


so as to correspond to the protrusions


24




a


and


24




b


of the fourth inner plane


14




i.






As shown in the figure, of the six planes making up the cube-shaped dice, engaging portions formed of recesses and protrusions are provided with the boundary areas Rb of four planes, thereby configuring a die capable of speedy assembly, and also capable of easily being opened onto a two-dimensional plane. Consideration may be made about the structure which has the engaging portions on the boundary areas Rb of the five inner planes.




With reference to

FIG. 2C

, the outer planes


11




o


and


16




o


of the first through sixth planes are mutually linked by the bridge portions Br, and the planes can be bent to the rear side in

FIG. 2C

on the bridge portions Br. Accordingly, the bridge portions Br might be called bending portions.




With

FIG. 2A

, only an arrangement wherein engaging portions are formed by combining recesses and protrusions that are provided only one apiece to each edge of each inner plane has been described so far, but a die can be assembled in the same manner as

FIG. 2A

by positioning multiple protrusions with spacing therebetween on one edge which is to be joined, and providing protrusions upon the other edge so as to be held between the multiple protrusions. In this case as well, making the protrusions on either edge to be of a size so as to not protrude out from the boundary areas Rb of the respective inner planes, is necessary in configuring a die which has a flat and polygonal form without protrusion in the event of being opened and also free of gaps when assembled.




Next, the method of manufacturing the die relating to the present invention will be described using the schematic configuration diagram of a mold shown in FIG.


4


. As shown in

FIG. 4

, the mold used with the present invention is configured of a lower mold


31


and an upper mold


32


. The lower mold


31


has raised portions


33


corresponding to the bridge portions Br. On the other hand, the upper mold


32


has inclined portions


34


at the portions corresponding to the boundary areas Rb of the respective inner planes, and gate portions


35


connected to the inclined portions


34


. As can be understood from the figure, the gate portions


35


of the upper mold


32


face the raised portions


33


of the lower mold


32


, thus configured so as to enable forming of the bridge portions Br between the planes. Note that the size of the mold is generally the same as that of the die described with reference to

FIGS. 2A through 2C

, and the engaging portions are also generally the same, so description thereof will be omitted here.




As shown in the figures, the opened die is such that the thickness of the bridge portions Br is extremely thin as compared to the first through sixth planes


11


through


16


. Accordingly, in the event that resin such as propylene or the like is injected from one place, the first through sixth planes and bridge portions Br might not be formed at a uniform thickness. With the mold according to the present invention, this is taken into consideration, and resin is injected into the mold from multiple inclined portions near the bridge portions Br, thereby sufficiently filling the gate portions for forming the extremely thin bridge portions Br with resin, as well. Incidentally, as for the method of injecting resin and forming the die, either injection molding or extrusion molding may be used.




After the mold shown in the figure is filled with resin and a predetermined amount of time elapses, opening the mold yields the die formed in the shape shown in

FIGS. 2A through 2C

.




A die according to another embodiment of the present invention will be described with reference to FIG.


5


. In

FIG. 5

as well, the same reference numerals denote the planes corresponding to FIG.


1


and

FIGS. 2A through 2C

, and the die shown in

FIG. 5

is arranged to be opened into a two-dimensional form the same as with that in

FIGS. 2A through 2C

. The die shown in the figure has a configuration whereby it can be opened into a two-dimensional form with a single touch. Accordingly, the die shown in the figure has a fourth plane


14


configured of first and second walls


41


and


42


. Of these, a button is provided upon the first wall


41


positioned within the die so as to pass through the second wall


42


and protrude therefrom, so that pressing the button


43


enables the first wall


41


to be pressed downwards.




Also, of the edges of the first wall


41


, the portions facing the first plane


11


, fifth plane


15


, and sixth plane


16


are each provided with recesses


44




a


,


44




b


, and


44




c


(


44




c


not shown) respectively. On the other hand, the first plane


11


, fifth plane


15


, and sixth plane


16


are each provided with protrusions


45




a


,


45




b


, and


45




c


, respectively facing the recesses


44




a


,


44




b


, and


44




c


. Also, the links between the fourth plane


14


and the third plane


13


, between the fifth plane


15


and the second plane


12


, between the second plane


12


and the third plane


13


, and between the first plane


11


and the sixth plane


16


, are of a hinged structure so as to open outwards as shown in the figure, centered on the axes thereof.




In the event that the configuration shown in the figure is used, in the state that the die is assembled the protrusions


45




a


,


45




b


, and


45




c


, of the first plane


11


, fifth plane


15


, and sixth plane


16


respectively are in a state of being engaged with the recesses


44




a


,


44




b


, and


44




c


of the fourth plane


14


.




In this state, in the event that the button


43


on the fourth plane


14


is pressed downwards in the drawing, the engaged state of the recesses


44




a


,


44




b


, and


44




c


and the protrusions


45




a


,


45




b


, and


45




c


is disengaged, such that the first plane


11


, fifth plane


15


, and sixth plane


16


respectively fall over in the near, left, and right directions in the figure, thus being opened into a two-dimensional form the same as that shown in

FIGS. 2A through 2C

. That is to say, the button


43


provided upon the fourth plane


14


, the recesses


45




a


,


44




b


, and


44




c


, and the protrusions


45




a


,


45




b


, and


45




c


make up an opening mechanism whereby opening can be performed with a single touch, simply by pressing the button


43


.




Accordingly, this configuration is advantageous in that simply pressing the button


43


opens the cubic dice onto a two-dimensional plane.




The above description has been made only regarding cases wherein the die is to be opened into the two-dimensional form shown in

FIGS. 2A through 2C

, but the present invention is not restricted to the two-dimensional form shown in

FIGS. 2A through 2C

; rather, the configuration may be such that is opened into forms shown in

FIGS. 6A through 6F

, for example. A cubic die can be assembled from any of the polygonal shaped patterns shown in

FIGS. 6A through 6F

, in the same manner as that shown in

FIGS. 2A through 2C

.




Referring to

FIGS. 7 and 8A

to


8


C, description will be made about another embodiment of the present invention. The die illustrated in

FIG. 7

is different from that illustrated in

FIG. 1

in that a clearance or a gap


50


is left between the fourth plane


14


and the first plane


11


. The die shown in

FIG. 7

is effective to be easily opened or flattened by inserting a fingertip or a fingernail into the gap


50


.





FIGS. 8A

,


8


B, and


8


C show an opened state of the die illustrated in FIG.


7


. It is readily understood with reference to

FIGS. 7 and 8A

to


8


C that the first inner plane


11




i


and the fourth inner plane


14




i


are adjacent to each other when the die is assembled from the opened state illustrated in FIG.


7


and that the gap


50


is left between the first and the fourth planes


11


and


14


in this embodiment, as mentioned in conjunction with FIG.


7


. In other words, the first plane


11


adjoins the fourth plane


14


with the gap


50


interposed therebetween, when the die is three-dimensionally assembled, as shown in FIG.


7


.




In order to leave the gap


50


between the first and the fourth planes


11


and


14


, it is to be noted that the first inner plane


11




i


has a narrow boundary area Rb


1


which is narrow in width as compared with the remaining boundary areas Rb. Stated otherwise, the width of the boundary area Rb


1


of the first inner plane


11




i


is narrower on the inclination angle portion than that of each of the remaining boundary areas Rb of the second through the sixth inner planes


12




i


to


16




i.






The illustrated narrow boundary area Rb


1


is positioned adjacent to the fourth inner plane


14




i


, on assembling the die. This means that the first inner plane


11




i


does not have an accurate square configuration and is different in configuration from the other inner planes


12




i


,


13




i


,


14




i


,


15




i


, and


16




i


. As a result, the first inner plane


11




i


is somewhat smaller in size than the remaining five inner planes


12




i


to


16




i


. In fact, the width of the boundary area Rb


1


of the first inner plane


11




i


is narrower than a half of each width of the remaining boundary areas Rb and may be smaller than 1 mm, for example.




Moreover, the die illustrated in

FIGS. 8A

to


8


C has protrusions and recesses greater in number than those illustrated in

FIG. 2

, so as to strongly keep a fastened or engaged state. In the illustrated example, two of the protrusions


23




p




1


and


23




p




2


are located on the boundary areas Rb of the third inner plane


13




i


while the recesses


25




gi


and


26




g




1


engaged with the protrusions


23




p




1


and


23




p




2


are located on the boundary areas of the fifth and the sixth inner planes


15




i


and


16




i


, respectively. Likewise, two recesses


24




g




1


and


24




g




2


are formed on the boundary areas of the fourth inner plane


14




i


. The corresponding protrusions


25




p




1


and


26




p




1


that are engaged with the recesses


24




g




1


and


24




g




2


are placed on the boundary areas Rb of the fifth and the sixth inner planes


15




i


and


16




i


, respectively. In addition, two of the protrusions


21




p




1


and


21




p




2


are added to the boundary area of the first inner plane


11




i


and the corresponding recesses


25




g




2


and


26




g




2


are placed on the boundary areas Rb of the fifth and the sixth inner planes


15




i


and


16




i


, respectively.




Thus, each set of the protrusions and the recesses may be called an engaging portion. In this event, it is readily understood that ten sets of the engaging portions are equipped with the illustrated die while five sets of the engaging portions are equipped with the die illustrated in FIG.


2


.




Although description has thus far been restricted to the dice that have five and ten sets of the engaging portions, the number of the engaging portions may be not smaller than four sets. For example, six, eight, and twelve sets of the engaging portions may be equipped with a die.




Making reference to

FIG. 9

, the external view of a die according to yet another embodiment of the present invention is shown. As can be understood from the figure, the die according to this embodiment has a regular tetrahedron shape configured of equilateral triangle planes.




Making reference to

FIG. 10

, the inner surface in a case wherein the regular tetrahedron die shown in

FIG. 9

is opened onto a two-dimensional plane is shown. Each plane of the regular tetrahedron die is formed of a center area and a boundary area, and the boundary area is provided with an inclined portion having an angle necessary for forming the regular tetrahedron (here, 30 degrees). In the example shown in

FIG. 10

, the die is opened such that the two-dimensional form forms a parallelogram. Note that for the engaging mechanism necessary for assembling the die opened such as shown in

FIG. 10

into a regular tetrahedron die, a mechanism the same as that shown in

FIGS. 2A through 2C

or

FIG. 5

can be used.




Making reference to

FIG. 11

, a case wherein the regular tetrahedron die shown in

FIG. 11

is opened onto another two-dimensional shape different from the shape shown in

FIG. 10

, is shown. In this case as well, a regular tetrahedron die can be assembled in the same manner as with FIG.


10


.




Thus, according to the present invention, a die, having a three-dimensional form which can be selectively opened two-dimensionally, can be obtained. Using such dice is advantageous in bringing greater variation to board games using dice, thus increasing user interest in board games.



Claims
  • 1. A method for manufacturing a die, which is configured of a polyhedron having multiple planes (11 through 16) of a similar shape and which can be opened into a continuous polygon area on a plane, each of the multiple planes having inclined boundary portions on one side (Rb1, Rb), the continuous polygon area being contiguous to one another through bridge portions (Br) connected between two adjacent ones of the multiple planes, the method comprising the steps of:preparing a mold (31, 32) having a first side and a second side opposite said first side, and a cavity therebetween in the form of said opened polyhedron and comprising inclined portions (34) which are formed on the one side and which correspond to the inclined boundary portions of the die, gate portions (35) connected to the inclined portions (34) on the one side, and raised portions (33) extended from an opposite side of the one side to define the bridge portions between the gate and the raised portions (35 and 33), the raised portions (33) forming linear grooves on the opposite side between the two adjacent ones of the multiple planes, said inclined boundary portions including a narrow inclined boundary portion (RB1) that is narrower in width than the remaining inclined boundary portions (Rb); and injecting a predetermined resin into said mold (31, 32) to obtain said die.
  • 2. A method for manufacturing a die according to claim 1, wherein said predetermined resin is polypropylene.
Priority Claims (1)
Number Date Country Kind
2000-40936 Feb 2000 JP
Parent Case Info

This is a divisional of application Ser. No. 09/785,325 filed Feb. 20, 2001; now U.S. Pat. No. 6,659,459 the disclosure of which is incorporated herein by reference.

US Referenced Citations (11)
Number Name Date Kind
1292188 Wheeler Jan 1919 A
3359657 Hedberg Dec 1967 A
3450408 Hagerman Jun 1969 A
3547444 William Dec 1970 A
3774339 Swett Nov 1973 A
3940142 Hinz Feb 1976 A
4097571 Cox Jun 1978 A
4489946 Burges Dec 1984 A
5151232 Thornthwaite et al. Sep 1992 A
5549198 Thiele et al. Aug 1996 A
6533275 Zaruba et al. Mar 2003 B2
Foreign Referenced Citations (7)
Number Date Country
2061853 Sep 1990 CN
2085676 Oct 1991 CN
1093033 Oct 1994 CN
8705084 Apr 1988 DE
2202159 Sep 1988 GB
7-112734 May 1995 JP
8-143034 Jun 1996 JP
Non-Patent Literature Citations (1)
Entry
JP Comic Strip Publication, pp. 95 and 96—The structure of the dice is shown in the comic and is self-expalnatory.