available at Kadon Enterprises

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 ; more about the origin of the polyspidrons here.

 

Polyspidrons is a puzzle with 54 pieces ; these pieces are polymultiforms ; they come from juxtaposition of 3 forms (the basic forms, green 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 an half-spidron that Dániel Erdély called "arm of spidron" and that I call "head of spidron".

 

The pieces below 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 to each polyspidron the colour that it has above, we have this tray :

Added to the 54 pieces, there are 5 little black triangles to fill the tray. If we tint with grey these little triangles and give to all the polyspidrons the same colour, we have, for example :

We can group 6 heads of spidrons to make a 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 one head more.

 

With the pieces of Polyspidrons, we can try to realize many figures with different sizes (the areas of the figures are red pointed ; the lengths are black pointed) :

triangles, hexagons, diamonds, dodecagons, rectangles, "suns", stars, trapeziums, "butterflies", "flowers", hexiamonds, and so on ...

For each of these figures, we can try to find, if it's possible, a solution without node, a solution with one node, 2 nodes, 3 nodes, and so on ...

 

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

So there are still 60 heads (so 10 nodes) and area 144 ; to see figures with area 144 click here.

 

Some figures, pointed by an asterisk, can be realized on the tray. Depending on the pieces which rest, the bottom of the tray can be one of these draws :