How to make wooden polyhedra
written by Hiroshi Nakagawa & Ikuro Sato
translated by Jon Flory Schrock
Chapter 1
At woodworking, the fundamental process primarily possible on a cube is called "chamfering."
Chamfering is possible at various angles.
Another one of the processes possible secondarily is "truncating."
In this chapter, I will how to develop all regular polyhedra and semiregular polyhedra from cubes by combining "chamfering" and "truncating."
Platonic solids
cube
tetrahedron
octahedron
dodecahedron
icosahedron
Archimedean solids
truncated tetrahedron
cub-octahedron
truncated octahedron
truncated cube
icosi-dodecahedron
truncated dodecahedron
rhomb-icosi-dodecahedron
great rhomb-icosi-dodecahedron
truncated icosahedron
great rhomb-cub-octahedron
rhomb-cub-octahedron
snub cube
snub dodecahedron
Polytopes
the 120-cell in 4 dimensions
the 600-cell in 4 dimensions
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Contents
1 Basics of Polyhedron Woodworking Techniques
1.1 Chamfering a cube
Meeting of a woodcrafter for a hobby and a mathematics lover
The fun of chamfering cubes
Woodworking procedures for chamfering cubes
1.2 From chamfering to truncating
Changing the depth of chamfering (rhombic dodecahedron)
Changing the angle of chamfering (hexagonal prism)
Truncating based on chamfering (truncated octahedron)
Variations in truncated cube
1.3 Chamfering with the golden ratio
Mastery of chamfering and truncating (regular icosahedron)
Impressive regular dodecahedron
1.4 Combination between chamfering and truncating
Truncation of a golden ratio system
Truncation of a regular tetrahedron
Chamfered truncated dodecahedron
Chamfered truncated cube
The most difficult twisting off
2 The fun of constructing wooden polyhedra
2.1 Construction of chamfered cubes (extracted)
2.2 Variety of the space-filling polyhedra (extracted)
2.3 Three-dimensional projection models of 4-polytopes
Development of four-dimensional 600-cell building blocks
3 Let's enjoy cutting the Platonic solids from styroform cubes (omitted)
