The number of strips needed to make the solid. This is the sum of the number of faces and the number of edges/connections.
The vertex configuration is a short-hand notation representing the sequence of faces around a vertex. For example (3.5.3.5) in the case of an icosidodecahedron means a vertex has 4 faces around it, alternating triangles and pentagons. With Platonic and Archimedean solids the vertex configuration is the same for all vertices.
Strips for face modules with more than four sides are preferably precreased as witches ladders. The wrapping method presented in the mini workshop is adequate for triangles and quadrangles.

Platonic and Archimedean solids

Didaktik-Kolloquium am 26. November 2010
Friedrich-Schiller-Universität Jena

Heinz Strobl www.knotologie.de

Edges / connections Polygonal faces Vertex
config.
Name Class Vertices Type 1 Type 2 3 4 5 6 8 10 Parts Creases Length
Tetrahedron Platonic 4 6 4 (3.3.3) 10 50 60
Hexahedron Platonic 8 12 6 (4.4.4) 18 102 120
Octahedron Platonic 6 12 8 (3.3.3.3) 20 100 120
Dodecahedron Platonic 20 30 12 (5.5.5) 42 198 240
Icosahedron Platonic 12 30 20 (3.3.3.3.3) 50 190 240
Truncated tetrahedron Archimedean 12 18 4 4 (3.6.6) 26 118 144
Cuboctahedron Archimedean 12 24 8 6 (3.4.3.4) 38 154 192
Truncated octahedron Archimedean 24 36 6 8 (4.6.6) 50 238 288
Truncated hexahedron Archimedean 24 36 8 6 (3.8.8) 50 238 288
Rhombicuboctahedron Archimedean 24 48 8 18 (3.4.4.4) 74 310 384
Icosidodecahedron Archimedean 30 60 20 12 (3.5.3.5) 92 388 480
Snub cube Archimedean 24 60 32 6 (3.3.3.3.4) 98 382 480
Truncated cuboctahedron Archimedean 48 72 12 8 6 (4.6.8) 98 478 576
Truncated icosahedron Archimedean 60 90 12 20 (5.6.6) 122 598 720
Truncated dodecahedron Archimedean 60 90 20 12 (3.10.10) 122 598 720
Rhombicosidodecahedron Archimedean 60 120 20 30 12 (3.4.5.4) 182 778 960
Snub dodecahedron Archimedean 60 150 80 12 (3.3.3.3.5) 242 958 1200
Truncated icosidodecahedron Archimedean 120 180 30 20 12 (4.6.10) 242 1198 1440
witches ladder!
Type 2 connections are necessary only for tetrahedron, hexahedron and octahedron. But they will increase the stability of Archimedean solids with polygons with many sides and too few triangles.
number of triangles
number of squares
number of pentagons
number of hexagons
number of octagons
number of decagons
Total length in units of width of all strips needed to make a polyhedron.