Pentakis dodecahedron

Pentakis dodecahedron

(Click here for rotating model)
Type Catalan solid
Coxeter diagram
Conway notation kD
Face type V5.6.6

isosceles triangle
Faces 60
Edges 90
Vertices 32
Vertices by type 20{6}+12{5}
Symmetry group Ih, H3, [5,3], (*532)
Rotation group I, [5,3]+, (532)
Dihedral angle 156°43′07″
arccos(−80 + 9√5/109)
Properties convex, face-transitive

Truncated icosahedron
(dual polyhedron)
Pentakis dodecahedron Net
Net
3D model of a pentakis dodecahedron

In geometry, a pentakis dodecahedron or kisdodecahedron is a polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron; that is, it is the Kleetope of the dodecahedron. Specifically, the term typically refers to a particular Catalan solid, namely the dual of a truncated icosahedron.