How to Make Gidipthi

Now it's time to learn how to build a star polychoron. First we would need to obtain access to a four dimensional world and get the poster board, 4-D scissors, coloring pencils, glue, and other useful 4-D items - I'll let you figure that one out :). Gidipthi is the head polychoron from category 22, it is the result of connecting gaddids to the star faces of sissid.
Gidipthi Piece Set Gidipthi Combo Set

Above are the four piece types of gidipthi, followed by combos, they were created using Stella4D. We could name the pieces and combos as follows:

the Four Piece Types

Bracket - green piece - comes from the gaddid cells, 3600 needed.

Pyramid - blue pentagonal pyramid - comes from the points of the sissid cells, 1440 needed.

Doe - blue dodecahedron - comes from the centers of the sissid cells, 120 needed.

Gem - red piece - comes from the corners of the ike cells, 1440 needed.

the Three Combos

Tripod - composed of three brackets, slightly folded inwards and glued where the gap was - green, 1200 needed.

Bowl - composed of one doe and 12 gems. Fold everything inwards and glue - looks like the dual of ti, but indented into a bowl (or a dish) with a doe shaped base - red walls, blue base, 120 needed.

Tegum - composed of two pyramids folded inwards, looks like a pentagonal tegum with center pentagon folded inwards - blue, 720 needed.

Fun With Brackets

Gidipthi Coming Together

The brackets can be put together into combos in two distinct ways. Three can form the tripods as seen in the combo pic, which fold inwards (concave). But it is also possible to put five together connected via chevron faces to form "drums" - these have an outward (convex) fold. The drums would work best for a double tab construction method, while the tripods work better for the single tab method (which I usually use). To the right shows a large cluster of brackets connected in a net, you can find both drums and tripods in it.

If we use the tripod combos, then all of the triangle faces need convex tabs and the chevron faces can have "half tabs" - divide the chevrons into two equal halves (4-sided shapes result) and let the right half have a convex tab and the left half without (assuming the two points point up). Connect the 1200 tripods together via the chevron faces, the half tabs should slide under the tabless half of its neighbor. The end result will be a nearly finished gidipthi with two types of holes - pentagonal tegum shaped holes and a "bumpy version of the dual of ti" shaped holes.

Filling the Gaps

Now let's make the bowls. Before being folded up, the bowls look like some wierd fruit bursting open. When folded, it will look like a dodecahedral based dish with stubby points at the top. No tabs are needed except for those that hold the bowl itself together. The 120 bowls will fit into the bumpy dual of ti shaped holes in the 3600-bracket structure that we made earlier. Now let's make the tegum combos, we need 720 and no tabs are needed here. Connect these into the tegum shaped holes by the tabs there. The model is now complete - toss the model in the air in a twirling motion, spin yourself about and catch it, saying "BOOYAH" to christen the finished model.

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Polyhedron Dude
Page created by Jonathan Bowers, 2016
e-mail = hedrondude at suddenlink dot net