Building polyhedra is a fascinating activity. The uniform polyhedra are particularly very nice. It is known that only 75 of these uniform polyhedra exist. The theory of uniform polyhedra is based on two excellent articles of Coxeter et.al from 1954 and of Skilling from 1975.

One book that is recommended to be read when building polyhedra is the book of Magnus Wenninger called Polyhedron Models published in 1971.

The topics that can be found on this webpage are:
1. Platonic Solids
2. Archimedean Solids
3. Stick Models
4. Puzzles
5. Rubic's Puzzles
6. Prototypes
7. Other Puzzles
8. Miscellaneous

Platonic Solids
First I built the 5 easiest polyhedra called the Platonic Solids. The platonic solids are the most beautiful polyhedra because they are completely regular.


tetrahedron
octahedron
cube
icosahedron
dodecahedron

Archimedean Solids
The next set of uniform polyhedra are the Archimedean Solids. There are 13 Archimedian Solids which are semi-regular.


truncated tetrahedron
truncated octahedron
truncated cube
truncated icosahedron
dodecahedron



cuboctahedron
icosidodecahedron 		



rhombicuboctahedron
rhombicosidodecahedron
rhombitruncated cuboctahedron
rhombitruncated icosidodecahedron



snub cube
snub dodecahedron

Stick Models
Besides the 5 Platonic solids and the 13 Archimedian solids, there are 57 other uniform polyhedra. These polyhedra are no longer regular or semi-regular and the faces can be star-shaped and intersect each other. Therefore, it is very interesting to build so-called stick models. A stick model exists for all the intersections of all the faces. If two faces intersect in a line, one gets the stick. If three faces intersect, one gets a node. The first stick model I built was the great stellated dodecahedron:


great stellated dodecahedron

If one looks closely, one sees in the middle


close-up great stellated dodecahedron

a dodecahedron and one gets the great stellated dodecahedron by extending the faces. Later on, we will see painted polyhedra which makes it more clear. The second stick model I built was the great icosahedron


great icosahedron

This is one of the most complex stick models. I built it without glue (just like the great stellated dodecahedron) and it started falling apart. Moreover, after some time I started building painted stick models which are much nicer. So I started to rebuild this stick model but I have not finished it yet. Below is the work in progress:


internal great icosahedron

The first stick model I started painting was the great ditrigonal icosidodecahedron.




If one looks closely, one sees 5 different colour nodes: dark green, red, light green, blue and orange. The dark green nodes form a dodecahedron, the red nodes form a icosahedron and the orange nodes form a dodecahedron again. Nodes have the same colour if they are the same (so if one puts them in a box one can not distinguish one from the other). It is interesting to see that nodes with the same colour have the same distance to the center of the polyhedron. This and other examples led me to the conjecture that the reverse of this is also true, i.e. if nodes have the same distance to the center of a polyhedron, then they must be the same (isomorphic). If it is not true for some nodes in one of the 75 uniform polyhedron, I would be very interested to see them. I have not been able to prove the conjecture yet but I am looking forward to somebody's opinion.

I also built the painted stick model of the great cubicuboctahedron




Wooden Puzzles


Rubic's Puzzles


Olympic Rings

Rubic's Cube

4x4x4 Rubic's Cube

Large Rubic's Cube

Rubic's Barrel

Rubic's Sphere

Prototypes



Other Puzzles




Miscellaneous