Nested Wooden Platonic Solids

Nested Wooden Polyhedra

Edge Length and Circumscribed Radius

Tetrahedron: E- 7 13/32": CR- 4.5

Cube: E-5 15/16": CR-5.15

Octahedron: E-7 13/32": CR-5.2

Icosahedron: E-7 13/32": CR-7

Dodecahedron: E-5": CR-7

Miter Angles and Saw Blade Bevel Angles

Tetrahedron: M-54.73°: SBBA-30°

Cube: M-35.26°: SBBA-30°

Octahedron: M-54.73°: SBBA-30°

Icosahedron: M-58.28°: SBBA-18°

Dodecahedron: M-31.71°: SBBA-18°

Building the nested Platonic Solids

I developed table saw sleds for the five Platonic Solids from the vertex of each Platonic solid. It made cutting the edge pieces of the Platonic Solids relatively easy. Gluing up the edge pieces correctly so the vertex's of each Platonic Solid were located in the correct theoretical location was more of a challenge than cutting the edge pieces. 

Here's vertex drawing for the Dodecahedron

Here's a drawing for the Saw Blade Bevel Angle for the Dodecahedron

Table saw sled for the Tetrahedron.

Table Saw Sled for the Cube.

Table Saw Sled for the Octahedron

Table Saw Sled for the Icosahedron

Table Saw Sled for the Dodecahedron

I created glue-up templates for the vertexs of each Platonic Solid to ensure the vertexs of the edges were in the correct theoretical locations. 

First glue-up for the Tetrahedron

First Glue-up for the Cube

Gluing-up the Cube

Gluing up the Tetrahedron inside the Cube. The four vertexs of the Tetrahedron touch four vertexs of the Cube.

First glue-up for the Octahedron

Final glue-up of the Octahedron inside the Cube. The 12 edges of the Octahedron touch the 12 edges of the Cube. 

First glue-up for the Icosahedron

First glue-up for the Dodecahedron

Second glue-up for the Dodecahedron

Gluing the Dodecahedron on top of the Icosahedron

The finished nested Platonic Solids.

For the edge bevel on the Platonic Solids, I used a straight edge with doubled-sided tape to attach the edge to the straight edge. 

Self Portraits with the nested Platonic Solids, recreating Luca Pacioli's famous portrait.