The snub dodecahedron is an Archimedean solid consisting of 92 faces (80 triangular, 12 pentagonal), 150 edges, and 60 vertices. It is sometimes called the dodecahedron simum (Kepler 1619, Weissbach and Martini 2002) or snub icosidodecahedron. It is a chiral solid, and therefore exists in two enantiomorphous forms, commonly called laevo (left-handed) and dextro (right-handed). The laevo snub dodecahedron is illustrated above together with a wireframe version and a net that can be used for its construction.
It is also the uniform polyhedron with Maeder index 29 (Maeder 1997), Wenninger index 18 (Wenninger 1989), Coxeter index 32 (Coxeter
et al. 1954), and Har'El index 34 (Har'El 1993). It has Schläfli
symbol s
and Wythoff symbol 
.
Some symmetric projections of the snub dodecahedron are illustrated above.
It is implemented in the Wolfram Language as PolyhedronData["SnubDodecahedron"].
An attractive dual of the two enantiomers superposed on one another is illustrated above.
The dual polyhedron of the snub dodecahedron is the pentagonal hexecontahedron, with which it is illustrated above.
It can be constructed by snubification of a dodecahedron of unit edge length with outward offset
 |
(1)
|
and twist angle
![theta=cos^(-1)[(64x^6+64x^5+800x^4+240x^3-800x^2-306x+59)_3].](/images/equations/SnubDodecahedron/NumberedEquation2.svg) |
(2)
|
Here, the notation 
indicates a polynomial root.
The inradius 
of the dual, midradius 
of the solid and dual, and circumradius 
of the solid for 
are given
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
The surface area is given by
![S=sqrt(15[95+6sqrt(5)+8sqrt(15(5+2sqrt(5)))]),](/images/equations/SnubDodecahedron/NumberedEquation3.svg) |
(9)
|
and the volume is given by the polynomial root
 |
(10)
|
