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)