convex semiregular polyhedra

The tutorials below, authored and narrated by vera viana, show examples of how to model* the Archimedeans that are convex semiregular polyhedra. These and other examples are included in my Doctoral Thesis.


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.


Truncated Tetrahedron, tT

2 ways of modelling the truncated tetrahedron from the tetrahedron (vera viana)

Truncated Cube, tC

modelling the truncated cube from the cube (vera viana)

Truncated Octahedron, tO

modelling the truncated octahedron from the octahedron (vera viana)
2 ways of modelling the truncated octaedron from the cube (vera viana)

Truncated Icosahedron, tI

(coming soon)


Truncated Dodecahedron, tD

(coming soon)


Rhombicuboctahedron, RCO

(coming soon)


Rhombicosidodecahedron, RID

(coming soon)


Rhombitruncated Cuboctahedron, rtCO

(coming soon)


Rhombitruncated Icosidodecahedron, rtID

(coming soon)


Snub Cube, sC

(coming soon)


Snub Dodecahedron, sD

(coming soon)


* The software used is Rhinoceros (version 6.0)