Archive for Platonic Solids

A Cube of 8 Tetrahedron

Posted in 1, geometry, Geometry Models, mid century modern with tags , , , , , , , , , , , , , , , , , , , , , on July 4, 2010 by rndmodelshop

A Cube of 8 TetrahedronTechnically its the same math as a cuboctahedron (8 triangles, 6 squares) but I made 8 tetrahedron in place of the triangles. This is symmetrical on all 6 planes, and it even looks nice standing up on a corner in a tripod stand.

This is typical of a 1950s – 60s Atomic Age ‘Mid Century Modern’ sculpture or light fixture.      9″ square, 48 pieces / Cherry, Walnut, Ebony wood stain or just Clear Polyurethane (shown).

For the complete polyhedron model index, please see my website.

4 Axis Stellated Tetrahedron in a Cube

Posted in 1, geometry, Geometry Models, mid century modern with tags , , , , , , , , , , , , , , , , , , , , , , on July 4, 2010 by rndmodelshop

Stellated 4 point Tetrahedron in a Cube displayed diagonal on a stand.

The 4 axis of a Stellated Tetrahedron (below) exactly correspond to 4 of the 8 interior vertices of a typical frame Cube. I just combined the 2 figures into one.  This can be displayed up on its corner, or just flat on a cube surface. It makes a very nice table top geometry sculpture.

The cube is 9″ flat, the entire sculpture is aprox 16″ tall in the stand. Each is made to orderand wood stained in cherry (red) walnut (brown) ebony (black) or natural as shown (clear coat polyurethane) that turns an amber honey color as the wood ages. Cube 12 pieces, tetrahedron 18 pieces, 30 pieces in total (plus stand).

For the complete polyhedron model index, please see my website.

Wood Tetrahedron Model “self-dual”

Posted in geometry, Geometry Models, mid century modern with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , on April 17, 2010 by rndmodelshop

All wood model of 2 Tetrahedrons woven together (aka Stella Octangula), one stained in cherry-wood the other left to a clear coat of polyurethane. These are great gift ideas for math teachers, engineers, students, plus those interested in “Atomic Age” 1950s interior design or Sacred Geometry. 

Most polyhedron have a dual, meaning they share or relate 1:1 with the number of vertices and / or planes. The tetrahedron (4 triangular surfaces, 4 vertices, 6 pieces each) is the only polyhedron that is its own self dual. This particular one I kept 2-tone for clarity, but I also make them in any one color. I have more versions on the website.

Wood Platonic Solids Models in the Physics Lab

Posted in 1, geometry, Geometry Models with tags , , , , , , , , , , , , , , , , , , on April 17, 2010 by rndmodelshop

Some of our wood Platonic Solids models in action. A friend looked all over the web for something like these for the classroom that would be much more durable and permanent than just card stock or construction paper. We found some color plastic ones, but not really what would look good in a university math lab, library or bookshelf.

Most things today are just computer generated line drawings, so there is something really cool about having a tangible geometric model to help show a concept. Like most other things, they are much easier to build in a batch then one at a time and that keeps them a lot more cost-effective.

Plethora of Polyhedron Models and Sculpture

Posted in 1, geometry, Geometry Models, mid century modern with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on April 14, 2010 by rndmodelshop

Usually these sculpture pieces are shipping out as quickly as we can make them so it’s not often we get a build up of so many all at once. This made a good group picture for scale. It’s hard to keep at least one of everything here since there are so many different pieces and combinations of pieces. Add in all of the combinations of wood stains and sizes and there are just too many!

When I don’t have a current order I work on new versions, truncations, or duals and various combinations of two or more. It’s really all about the table saw miter and getting all 3 axis angles dead on, then making it repeatable a week, month or a year later without having to re-invent the wheel every time!

Wood Dodecahedron Sculpture (woven-2)

Posted in geometry, Geometry Models, mid century modern with tags , , , , , , , , , , , , , , , , , , , , , , on April 13, 2010 by rndmodelshop

These are great table top or hanging decor pieces for 1950s “Atomic Age” Mid Century Modern houses. They were common plastic or wood light fixtures in the classic 1950s “Googie” coffee shops.This is a Dodecahedron formed by 60 inter-woven pieces of wood. They form 12 small pentagons on each flat plane, and 12 great pentagons that wrap around the 5 adjacent planes. Each intersection is a compound miter notch cut only halfway thru the wood so the 2 pieces press together with a friction fit, similar to how Lincoln Logs nest together in their notches. I have more pieces like these on my website with alot more to come!

Wood Platonic Solids Models set for education & display

Posted in Geometry Models with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on April 12, 2010 by rndmodelshop

These are 9″ tall wood models of the 5 Platonic Solids I make for Math, Astronomy and Physics classroom visual aids. They are all compound mitered on all 3 axis at the vertices for maximum glue strength. They also make great office & home decor pieces. 9″ max on any axis seems to be the best for a 12″ cube box to ship them in. I have alot more geometry pieces on my website. Typically when I set up the saw for each of the compound miters, I make them in batches of 10 or so to keep down all of the set up time involved.

From left: Octahedron, Dodecahedron, Tetrahedron, Icosahedron & Cube. These are just clear polyurethane coated for clarity in the photos, but I also wood stain & clear seal them to match someones home or office decor.

 Wood Octahedron Model / 8 triangle planes, 6 vertices and 12 pieces.

 Wood Dodecahedron Model / 12 pentagon faces, 20 vertices and 30 pieces.

Wood Tetrahedron Model / 4 triangle planes, 4 vertices and 6 pieces.

Wood Icosahedron Model / 20 triangles, 12 vertices and 30 pieces.

Wood Cube Model / 6 squares, 8 vertices and 12 pieces.