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

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Heinz Strobl www.snapology.eu

			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.