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The Bosch d120

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The d120 or 120-sided die is the dual of the truncated icosidodecahedron. It is known by various other names: disdyakis triacontahedron, hexakis icosahedron or decakis dodecahedron.

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In 2016, the first injection mold for a d120 was considered by Dice Lab. For perfect balance, they wanted the following properties:

1. The sum of any of 60 opposing faces = 121.

2. The sum at any of the 30 4-vertices = 242.

3. The sum at any of the 20 6-vertices = 363.

4. The sum at any of the 12 10-vertices = 605.

This Demonstration uses the Bob Bosch solution, labeling the 120 faces so that all similar vertices have a similar sum. Choose any of the 62 vertices or pair of opposing faces to highlight the digits.

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Contributed by: Ed Pegg Jr (October 12)
Open content licensed under CC BY-NC-SA

Details

In the initialization, a method for using quaternions to build the faces is shown.

Reference

[1] "d120 and d48." The Dice Lab. (Sep 29, 2023) www.mathartfun.com/thedicelab.com/d120.html.

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