Convex uniform polyhedra have regular faces and are isogonal, which means that they are transitive in their vertices. They are dividable into: regular polyhedra (5, isoedral and isotoxal, commonly known as the Platonic), quasiregular polyhedra (2, isotoxal and Archimedeans, in which each face is completely surrounded by faces of a different type) and semiregular poyhedra, which comprises the remaining 11 Archimedeans and the infinite families of the semiregular prisms and antiprisms.
The quasiregular polyhedra, obtained from rectification of the convex regular, are dealt with in this webpage. Here, I will first explain how to model the 5 Archimedeans from the convex regular through uniform truncation:
- the truncated tetrahedron from the regular tetrahedron;
- the truncated cube from the cube;
- the truncated octahedron from the octahedron, and from the cube.
The tutorials below show examples of how to model* the Archimedeans that are convex semiregular polyhedra. These and other examples are included in my Doctoral Thesis (in Portuguese).
Truncated Tetrahedron, tT
Truncated Cube, tC
Truncated Octahedron, tO
Truncated Icosahedron, tI
Truncated Dodecahedron, tD
Rhombitruncated Cuboctahedron, rtCO
Rhombitruncated Icosidodecahedron, rtID
Snub Cube, sC
Snub Dodecahedron, sD
* The software used is Rhinoceros (version 6.0)