Roof Framing Geometry

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.