Snub disphenoid

Snub disphenoid
Type	Deltahedron Johnson J83 – J84 – J85
Faces	12 triangles
Edges	18
Vertices	8
Vertex configuration	${\displaystyle 4\times (3^{4})+4\times (3^{5})}$
Symmetry group	${\displaystyle D_{2\mathrm {d} }}$
Dihedral angle (degrees)	four edges: 164.2° eight edges: 121.74° six edges: 96.2°
Dual polyhedron	Elongated gyrobifastigium
Properties	convex, elementary
Net

In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape is also called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron.

The snub disphenoid can be visualized as an atom cluster surrounding a central atom, that is, the dodecahedral molecular geometry. Its vertices may be placed on a sphere and can also be used as a minimum possible Lennard-Jones potential among all eight-sphere clusters. The dual polyhedron of the snub disphenoid is the elongated gyrobifastigium.