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.