  Göttingen Collection of Mathematical Models and Instruments

# Snub dodecahedron

### Model 483

 Category: B II 188

### Description

(12+20+60)-plane polygon with 60 vertices, polar to the pentagonal hexecontahedron.

Inscribed (12+20+60)-plane polygon with 60 vertices The snub dodecahedron is circumscribed by

12 pentagons + 20 triangles + 60 triangles = 92 faces.

It has 5·12 = 60 vertices and 150 edges. At each vertice four triangles and one pentagon are meeting (3,3,3,3,5).

The snub dodecahedron is one of 13 Archimedean solids, see also 482.

pentagonal hexecontahedron The snub dodecahedron is polar (dual) to the pentagonal hexecontahedron. To create this new solid a sphere is inscribed in the snub dodecahedron such that the sphere touches each of the faces in exactly one point. These points of contact create the vertices of the dual solid. By connecting these 90 vertices 60 hexagons are formed. These hexagons are the faces of the pentagonal hexecontahedron. The number of edges remains the same during the transformation into the dual solid, while the number of vertices and faces is exchanged.

There are 11 Archimedean solids in the collection.

 472 Truncated tetrahedron inscribed in a tetrahedron 473 Truncated octahedron inscribed in an octahedron 474485 Cuboctahedron 474 inscribed in an octahedron485 inscribed in a cube 475 Truncated cube inscribed in an octahedron 476 Rhombicuboctahedron inscribed in a cube 478 Truncated icosahedron inscribed in an icosahedron 479 truncated dodecahedron inscribed in a dodecahedron 480481 Icosidodecahedron 480 inscribed in a dodecahedron481 inscribed in an icosahedron 482 Rhombicosidodecahedron 483 Snub dodecahedron 484 Truncated cube inscribed in a cube

The truncated icosidodecahedron and the lost truncated cuboctahedron are not included in the collection.

Showcase of this model is Case number 21

### References

Heesch, H.. Comm.Math.Helv, 6, n=5, Case 2b.

Hess, E.(1883). Kugelteilung, Teubner, mit Figuren, §43, fig. 25.