Building Wooden Archimedean Solids
da Vinic's Polyhedra Φ Project #2
Cuboctahedron: Edge Length 2.75": Circumradius 2.75"
Small Rhombicuboctahedron: Edge Length 2.75": Circumradius 3.84714"
Snube Cube: Edge Length 2.75": Circumradius 3.6952"
Rhombicosidodecahedron: Edge Length 2.75": Circumradius 6.1406"
The study of polyhedra develops spatial reasoning and imagination while providing the foundation for points in 3D space to a vertex-plan view drawing of 2D points. Precise geometric forms are powerful examples to show off one's mastery, as they require a clear understanding of the relationship between 3D objects and 2D projections.[George Hart: 2022]
Left to right: Golen Rectangle Rhombicosidodecahedron, Standard Rhombicosidodecahedron, Small Rhombicuboctahedron, Snube Cube, and Cuboctahedron.
Not museum quality, but they look great. I gave it my best shot with my old eyes. I found it easy to cut the polygon pieces, but a real challenge to glue the polygon shapes with a perfect fit. Then I found myself over-sanding on some of the polygon faces, which creates ridges on the adjoining polygon faces.
Rhombicosidodecahedron
Material: Squares-Yellowheart, Equilateral Triangles-Bubinga, Pentagons-Bolivian Rosewood
Archimedean Solid Rhombicosidodecahedron table saw blade tilt angle settings:
12 Pentagons
20 Equilateral Triangles
30 Squares
Dihedral Angle
159.09484°
Polygon Saw Blade Bevel Angles
Equilateral Triangle: 7.62263°
Square: 13.28252°
Dihedral Angle
148.28252°
Polygon Saw Blade Bevel Angles
Pentagon: 18.43495°
Square: 13.28251°
Polygon Table Saw Sleds
Glue up Templates for Rhombicosidodecahedron
Cut and glue time: 3 Days
The next three Archimedean Solids were built using this printout for the blade tilt angles. You lay a piece of wood on the paper and scribe the blade tilt angles. Cut the piece of wood with a compound miter saw. Basically, sneak up on the scribe mark on the wood for the blade tilt angles.
Small Rhombicuboctahedron
Material: Equilateral Triangles-Yellowheart, Squares-Bubinga
Archimedean Solid Small Rhombicuboctahedron table saw blade tilt angle settings:
18 Squares
8 Equilateral Triangles
Dihedral Angle
144.73561°
Polygon Saw Blade Bevel Angles
Square: 22.5°
Equilateral Triangle: 12.76439°
Dihedral Angle
135.00°
Polygon Saw Blade Bevel Angles
Square: 22.5°
Square: 22.5°
Small Rhombicuboctahedron Glue Up
Cut and glue time: 1 Day
Snub Cube
Material: Equilateral Triangles-Yellowheart, Squares-Bubinga
Archimedean Solid Snub Cube table saw blade tilt angle settings:
6 Squares
32 Equilateral Triangles
Dihedral Angle
153.2345877°
Polygon Saw Blade Bevel Angles
Equilateral Triangle: 13.382706°
Equilateral Triangle: 13.382706°
Dihedral Angle
142.98343007°
Polygon Saw Blade Bevel Angles
Square: 23.63386°
Equilateral Triangle: 13.382706°
Snub Cube Glue Up
Cut and glue time: 1 Day
Cuboctahedron
Material: Equilateral Triangles-Yellowheart, Squares-Bolivian Rosewood
Archimedean Solid Cuboctahedron table saw blade tilt angle settings:
6 Squares
8 Equilateral Triangles
Dihedral Angle
109.471220635°
Polygon Saw Blade Bevel Angles
Equilateral Triangle: 19.47122°
Square: 35.26439°
Cuboctahedron Glue Up
Cut and glue time: 4 Hours
Only 9 more Archimedean Solids to build.
