Building Wooden Archimedean Solids

da Vinic's Polyhedra Φ Project #4

Icosidodecahedron: Edge Length 2.75": Circumradius 4.4495"

Truncated Dodecahedron: Edge Length 2.75": Circumradius 8.1659"

Truncated Icosidodecahedron: Edge Length 2.75": Circumradius 10.4563"

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]

Top Row Left to right: Rhombicosidodecahedron, Small Rhombicuboctahedron, Snube Cube, and Cuboctahedron. Next row, left to Right: Truncated Cuboctahedron, Truncated Cube, Truncated Octahedron, and Icosidodecahedron.

Icosidodecahedron

Material: Equilateral Triangles-Yellowheart, Pentagons-Sapele

Archimedean Solid Icosidodeachedron table saw blade tilt angle settings:

12 Pentagons

20 Equilateral Triangles

Dihedral Angle

142.62263°

Polygon Saw Blade Bevel Angles

Equilateral Triangle: 10.8123169°

Pentagon: 26.56505°

Glue up Templates for Icosidodecahedron

Cut and glue time: 5 Hours.

Video showing the steps to build the Icosidodecahedron

Truncated Dodecahedron

Material: Equilateral Triangles-Yellowheart, Decagons-Sapele

Archimedean Solid Truncated Dodecahedron table saw blade tilt angle settings:

12 Decagons

20 Equilateral Triangles

Dihedral Angle

142.62263°

Polygon Saw Blade Bevel Angles

Equilateral Triangle: 5.6599°

Decagon: 31.71747°

Glue up Templates for Truncated Dodecahedron

Cut and glue time: 6 Hours.

Checking the exterior angle of the Decagon polygon, 144°.

Truncated Icosidodecahedron

Material: Equilateral Triangles-Yellowheart, Decagons-Sapele, Hexagons-Purpleheart

All of the Archimedean Solids have the same edge length, 2.75". Here you can see how much bigger the Truncated Icosidodecahedron is, compared to the other Archimedean solids. 

Archimedean Solid Truncated Icosidodecahedron table saw blade tilt angle settings:

12 Decagons

30 Squares

20 Hexagons

Dihedral Angle

159.09484°

Polygon Saw Blade Bevel Angles

Square: 7.62263°

Hexagon: 13.28252°

Dihedral Angle

142.62263°

Polygon Saw Blade Bevel Angles

Decagon: 24.09°

Hexagon: 13.28251°

Glue up Templates for Truncated Icosidodecahedron

Cut and glue time: 16 Hours.

Checking to make sure the Decagon exterior angle is 144°

Use a table saw to bevel one edge of the material. Then mark one edge of the hexagon. The material will have one edge beveled, before you mark the one edge of the hexagon. 

Miter angle 30°

Cut the one edge. So, you will have two edges with the correct miter and bevel angle, before you cut the other four sides with the table saw sled. 

The blue tape technique did not work. The pieces were too heavy to stay in place.

Here I built a jig to hold the pieces, but then I decided to use a pin nailer(23 gauge) to assemble the pieces, and I didn't use the jig.

First Half pin nailed and glued together. 

I left out the squares to make it easier to assemble. 

Some of the squares are proud of the adjacent polygon faces. Just needs more sanding on the squares to flush up the polygon faces.