First, create a bevel on one edge of the material. Here I have a 2" x 2" x 12" piece of Purpleheart wood. With one edge ripped to 19.47°.
Next, lay the material on the compound miter saw with the table saw edge bevel facing you. The miter angle is 30°, and the blade tilt is 19.47°.
After the first cut, turn the material upside down. The table saw edge bevel will be facing the compound miter saw fence. Lay out the desired Tetrahedron edge length at a 30-60° angle from the back edge of the material. In this example, the edge length is 2 1/8".
Then make the cut to cut the Solid Tetrahedron.
I was able to cut 4 solid Tetrahedrons out of each 12" piece of material.
Remember to flip the material back to the starting position each time you cut the Tetrahedron.
Video showing the complete process for cutting the Solid Tetrahedron.
Roman Dodecahedrons Made out of Wood
Platonic Solid Dodecahedron
12 Pentagonal Faces
Roman Dodecahedron made out of Ash.
The Roman Dodecahedron is painted with metallic Silver, and the rings are painted with carbon black.
This Roman Doecahedron made out of Walnut has a 2 1/2" hole in each face.
Cut 12 Pentagons with a 31.71° blade tilt for the edge bevel. (Note: This picture is from an Archimedean Solid. It does not have the 31.71° blade tilt.)
Drill a circle 1/8" deep with a 3" diameter drill bit.
Drill a circle 1/8" deep with a 2 1/4" diameter drill bit.
Drill a hole with a 1 1/2" diameter drill bit.
Glue up the pentagon pieces.
Add balls at each vertex of the Dodecahedron. I drilled a 3/16" hole at each vertex. Then, I use instant glue to attach the miller dowels, with a ball at each vertex.
I used Miller wood screw dowels with a 1/2" maple ball glue to each dowel.
Video showing the complete process for the Roman Dodecahedra made out of wood.
Truncated Octahedron Fish Tank
With Plato, Archimedes, and Euclid, goldfish.
Archimedean Solid Truncated Octahedron
6 Squares
8 Hexagons
Dihedral Angle
125.264389683°
Polygon Saw Blade Bevel Angles
Square: 19.47122°
Hexagon: 35.26439°
Here are some of the techniques I used to build the Truncated Octahedron fish tank. The Truncated Octahedron is built with 6 squares and 8 hexagons. You can use a hexagon table saw sled or a compound miter saw to cut the 8 hexagons with a 35.26 edge bevel angle. The 6 squares have a 19.47 edge bevel angle.
I used the
Amana Tool LB10801 Carbide Tipped Non-Melt Plastic 10 Inch D x 80T M-TCG, -2 Deg, 5/8 Bore, Circular Saw Blade
I felt it cut the 1/2” polycarbonate material like butter.
Cut a block of wood with a 32.26° angle, for the blade tilt for the Hexagons.
Before I used the table saw sled, I edge beveled one edge of the material with the table saw. Then I cut the material into 6" pieces. Then I set the miter saw to 30°, with a blade tilt of 35.26°, and cut one edge of the hexagon. So, I would have two edges mitered and beveled before I used the hexagon table saw sled.
Rotate the material until all its edges form a hexagon.
The squares were shaped in the same way as the hexagons were.
Use tape to glue the pieces of the Truncated Octahedron together.
After the pieces are cut, I used Acrylic Cement along the inside edges. It fuses the polycarbonate material together. Then I used fish-safe silicone along the inside edges.
This Truncated Octahedron fish tank is probably the only one in existence. You could also use any of these Archimedean Solids as a fish tank.
Cuboctahedron,
Small Rhombicuboctahedron,
Snub Dodecahedron,
Icosidodecahedron,
Truncated Cube,
Truncated Icosahedron
If I were to build the fish tank again, I would use 1/4" polycarbonate material. And try to get less glue on the faces of the pieces.
Wednesday, August 27, 2025
Building Wooden Archimedean Solids
da Vinic's Polyhedra Φ Project #5
All 13 of the Archimedean Solids are now built out of wood.
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]
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.
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.
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.
