Polyspidrons

Publié le par FERROUL Jacques

To have Polyspidrons™, go to

 Kadon enterprises

(If you want that all the pieces of your Polyspidrons have the same colour, specify that during the order)

Since the 80th years I worked about polyforms called now polyiamonds, and about polymultiforms, among them the polyiapons ... In 2006, I added to these polymultiforms half-spidrons: the Spidron was created by Dániel Erdély  ( see Spidronatlanta and SpidroNew) ; afterwards I shall call "head of spidron" an half-spidron and "node of spidrons" the hexagon made with 6 heads of spidrons.

More about the polyiamonds, the polyiapons and the spidrons (in french, but soon in english) in KAP’ROMPILOJ.

Jacques FERROUL

                                                                      jacques.ferroul@laposte.net 



Polyspidrons is a puzzle with 54 pieces ; here they are in the tray :

These pieces are polymultiforms ; they come from juxtaposition of 3 forms (the basic forms, yellow below) ; the 3 basic forms have the same area ; afterwards I shall take this area as unit of area.

These 3 forms are monospidrons. The 3rd form is called "head of spidron".

The blue pieces above are composed of 2 basic pieces : they are bispidrons ; there are 4 bispidrons without head, 3 bispidrons with 1 head and 3 bispidrons with 2 heads.

So there are 3 monospidrons and 10 bispidrons ; the trispidrons are 41 in number :

Above, the 12 trispidrons without head and the 12 trispidrons with 1 head.

Below, the 12 trispidrons with 2 heads and the 5 trispidrons with 3 heads :

If we give at each polyspidron the colour that it has above, we have this tray :

We can group 6 heads of spidrons to make an hexagon that I call "node of spidrons" ; if we arbitrarily choose a direction, we can have

a positive node                     or a negative node      

If we underline these nodes in the tray, we obtain : 

There are 7 positive nodes and 3 negative nodes ; but the important thing is their number : there are 10 nodes of spidrons ; if we number the heads of all 54 polyspidrons, we find 61 : so really 10 nodes of 6 heads and 1 head more.

If we look now at the areas, the 54 pieces cover area of 146 ; to do interesting forms, I arbitrarily choose take off 1 head and another monospidron ( or  a bispidron with 1 head), that is : 

So there are still 60 heads (10 nodes) and area 144 ; almost all the challenges that I give have this convention.*

The tray was modified to be able realize some challenges on the tray ; there are 5 little black triangles, which I put grey below to see them :

Depending on the pieces which rest, the bottom of the tray can be one of these draws :

*   From the challenge 035, some challenges will have area 145 : the piece which rests will be inevitably the monospidron "head of spidron". These challenges will be pointed by the sign + (ex : 035 +) and by a red head of spidron.

If we can realize them on the tray, the bottom of the tray will be :          

 

* From the challenge 068, some challenges will have area 146, so they uses all the pieces of Polyspidrons. These challenges will be pointed by ++. 

 

*  From the challenge 044, some challenges will have area 143 ; there are 23 possibilities for the piece(s) which rest(s) :

 These challenges will be pointed by the sign - (ex : 044 -) and above all will be green coloured.

Publié dans English

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