Platonic and Archimedean solids
Models of every Platonic and Archimedean solid can be built with Geomag. If you want to refresh your memory, MathWorld pages Platonic Solid and Archimedean Solid have lots of information, including three-dimensional models, plane nets, formulae, etc. This page (in Spanish) is also a handy reference.
There are five Platonic solids and thirteen Archimedean ones. Adding the pentagonal prism and antiprism gives twenty convex uniform polyhedra. There are at least 60 non-convex uniform polyhedra which, as far as I know, cannot be built with Geomag (see the MathWorld article Uniform Polyhedron).
In the following picture all eighteen solids appear, ordered by size. Building some of them is very quick and straightforward, while others are more involved and require auxiliary structures.
Body edges are made of blue rods, and auxiliary structures, required for building hexagonal, octagonal, and decagonal faces, are made of silver rods. One can tell polygons which are true faces of the bodies from auxiliary ones in this manner:
  • Pentagons and squares: we use red panels for true faces, yellow panels for auxiliary ones.
  • Triangles: we use green panels for true faces, no panels for auxiliary ones.
  • Rhombuses: all of them are yellow and part of hexagonal true faces.
GEOMAG constructions: Platonic and Archimedean solids
Platonic and Archimedean solids
3326 pieces: 820 balls, 1728 rods, 84 pentagons, 282 squares, 180 rhombuses, 232 triangles (16.34 kg)
The solids are named as follows, front row to rear row, left to right (links go to individual pictures, below in this page):
first row regular tetrahedron, regular octahedron, cube or regular hexahedron, regular icosahedron, cuboctahedron, truncated regular tetrahedron, snub cuboctahedron, regular dodecahedron, rhombicuboctahedron
second row truncated regular octahedron, icosidodecahedron, truncated cube, snub icosidodecahedron, rhombicosidodecahedron
third row rhombitruncated cuboctahedron, truncated regular icosahedron, truncated regular dodecahedron, rhombitruncated icosidodecahedron
The following four pictures show more detail. The provided higher resolution versions of the last three pictures use about the same scale as the first one:
GEOMAG constructions: Tetrahedron and truncated tetrahedron
Tetrahedron and truncated tetrahedron
GEOMAG constructions: Snub cuboctahedron and icosidodecahedron
Snub cuboctahedron and icosidodecahedron
GEOMAG constructions: Cube and octahedron subfamily
Cube and octahedron subfamily
GEOMAG constructions: Dodecahedron and icosahedron subfamily
Dodecahedron and icosahedron subfamily
Finally, individual pictures of each body. When no auxiliary structures are required, ball, rod, and panel quantities match those of vertices, edges, and faces. When there are auxiliary structures, quantities don't match. In the last cases, we specify in brackets the quantities of vertices, edges, and faces.
For instance, (12v, 18e, 4f6, 4f3) means: 12 vertices, 18 edges, 4 hexagonal faces, and 4 triangular faces.
Platonic solids:
GEOMAG constructions: Regular tetrahedron
Regular tetrahedron
14 pieces: 4 balls, 6 rods, 4 triangles (65.08 g)
GEOMAG constructions: Cube or regular hexahedron
Cube or regular hexahedron
26 pieces: 8 balls, 12 rods, 6 squares (136.12 g)
GEOMAG constructions: Regular octahedron
Regular octahedron
26 pieces: 6 balls, 12 rods, 8 triangles (112.96 g)
GEOMAG constructions: Regular dodecahedron
Regular dodecahedron
62 pieces: 20 balls, 30 rods, 12 pentagons (349.00 g)
GEOMAG constructions: Regular icosahedron
Regular icosahedron
62 pieces: 12 balls, 30 rods, 20 triangles (256.60 g)
Archimedean solids:
GEOMAG constructions: Truncated regular tetrahedron
Truncated regular tetrahedron
68 pieces: 16 balls, 36 rods, 12 rhombuses, 4 triangles (326.56 g)
(12v, 18e, 4f6, 4f3)
GEOMAG constructions: Truncated cube
Truncated cube
130 pieces: 32 balls, 72 rods, 18 squares, 8 triangles (651.32 g)
(24v, 36e, 6f8, 8f3)
GEOMAG constructions: Truncated regular octahedron
Truncated regular octahedron
122 pieces: 32 balls, 60 rods, 6 squares, 24 rhombuses (602.68 g)
(24v, 36e, 8f6, 6f4)
GEOMAG constructions: Truncated regular dodecahedron
Truncated regular dodecahedron
482 pieces: 120 balls, 270 rods, 12 pentagons, 60 squares, 20 triangles (2.46 kg)
(60v, 92e, 12f10, 20f3)
GEOMAG constructions: Truncated regular icosahedron
Truncated regular icosahedron
302 pieces: 80 balls, 150 rods, 12 pentagons, 60 rhombuses (1.52 kg)
(60v, 92e, 20f6, 12f5)
GEOMAG constructions: Cuboctahedron
50 pieces: 12 balls, 24 rods, 6 squares, 8 triangles (231.88 g)
GEOMAG constructions: Icosidodecahedron
122 pieces: 30 balls, 60 rods, 12 pentagons, 20 triangles (588.40 g)
GEOMAG constructions: Rhombicuboctahedron
98 pieces: 24 balls, 48 rods, 18 squares, 8 triangles (469.72 g)
GEOMAG constructions: Rhombicosidodecahedron
242 pieces: 60 balls, 120 rods, 12 pentagons, 30 squares, 20 triangles (1.18 kg)
GEOMAG constructions: Rhombitruncated cuboctahedron
Rhombitruncated cuboctahedron
314 pieces: 80 balls, 168 rods, 42 squares, 24 rhombuses (1.59 kg)
(48v, 72e, 6f8, 8f6, 12f4)
GEOMAG constructions: Rhombitruncated icosidodecahedron
Rhombitruncated icosidodecahedron
782 pieces: 200 balls, 420 rods, 12 pentagons, 90 squares, 60 rhombuses (3.98 kg)
(120v, 180e, 12f10, 20f6, 30f4)
GEOMAG constructions: Snub cuboctahedron
Snub cuboctahedron
122 pieces: 24 balls, 60 rods, 6 squares, 32 triangles (519.16 g)
GEOMAG constructions: Snub icosidodecahedron
Snub icosidodecahedron
302 pieces: 60 balls, 150 rods, 12 pentagons, 80 triangles (1.31 kg)