How to Make Padohi

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 :). Padohi is the head polychoron from category 21, it is the result of runcinating sishi.
Padohi Piece Set Padohi Combo Set

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

the Seven Piece Types

Cage - large blue hollow soccer ball - comes from the ike cells, 120 needed.

Sissid - yellow star - It is the entire sissid cell, 120 needed.

Wedge - largest of the red pieces - comes from the corners of the stip cells, 7200 needed.

Block - green piece near the top - comes from the corners of the trip cells, 7200 needed.

Pyramid - blue pentagonal pyramid - comes from the corners of the ike cells, 1440 needed.

Ditrigonal - lower green piece - comes from the triangle faces of the trip cells, 2400 needed.

Tiny - tiny red splinter - comes from the stip cells at the square-square edges, 3600 needed.

the Four Combos

Wing - composed of two wedges slightly folded inwards - red of course, 3600 needed.

Tripod - composed of three blocks, slightly folded inwards and glued where the small gap was - green, 2400 needed.

Tetrahedral - composed of four ditrigonals and folded inwards and glued - looks like a tut with center dimpled inwards slightly - green, 600 needed.

Trigonal - composed of three tinies folded inwards slightly and glued, looks like a triangle tegum with center wedge folded inwards - red, 1200 needed.

Skeletal Structure

First, let's make a xhi shaped skeletal structure. This structure will have 120 golden ratio tis (truncated icosahedra) which looks like a filled in cage. Make 120 of these large pentagoned tis and connect them by the pentagons and have tabs connected to the ditrigons. Score the tabs so they can fold convexly. The skeletal structure doesn't need coloring due to it being covered up later. It will look like a semiuniform version of the polychoron xhi, but with the inter-connected lattice of tuts missing.

Building the Mounds

We will need to build 120 "mounds" which pierce through bases (cages). Each mound consists of a sissid, 30 wing combos, 20 tripod combos, and 12 pyramids. The mound when finished will pierce through a cage which acts as the base of the mound. First take a sissid surrounded by tabs folded convexly. Then make 30 wings where all of the exposed 4-sided faces of it have tabs that fold convexly. The wings will fit between two star arms of the sissid, glue there. Next make the 20 tripods. The pentagonal and equilateral triangle faces of them will have tabs that fold convexly. Glue these in between three wings, they will be in the three-fold regions of the sissid. Next make 12 pyramids with no tabs needed. They connect to the equit shaped faces of the tripod combo and will be adjacent to the points of the sissid. The mound is complete. Next we need to add the base. Cut out a cage, this is going to be a bit tedious. Make sure to add convex tabs to the small isosceles triangle face facing inwards on the cage, they will connect to the small faces on the wings. The pentagonal tabs of the tripod combos will connect to the isosceles pentagon faces on the inside of the cage. Now the mound is set with a base. Make 120 mounds and glue the bottom of the cage part to glue them to the ti shaped faces of the skeletal frame which the mound will completely cover them.

Finishing Padohi

It's starting to shape up, only the tut shaped regions are missing. Now make the 600 tetrahedral combos, put convex tabs on the small trigonal faces. These tetrahedral combos will glue into the tut shaped gaps on the skeleton, via the tabs there. They will look like tut shaped indentions. Finish the model with the 1200 tiny trigonal combos which will fit between two tetrahedral combos. The model is complete - don't forget to toss the model in the air so it twirls before catching it as a way to christen the finished model.

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