The dodecahedron  Statistics

 genus c 0, orientable Schläfli formula c {5,3} V / F / E c 20 / 12 / 30 notes    vertex, face multiplicity c 1, 1 Petrie polygons 6, each with 10 edges antipodal sets 10 of ( 2v ), 6 of ( 2f; p1 ), 15 of ( 2e ) rotational symmetry group A5, with 60 elements full symmetry group A5×C2, with 120 elements its presentation c < r, s, t | r2, s2, t2, (rs)5, (st)3, (rt)2 > C&D number c R0.3′ The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the icosahedron.

Its Petrie dual is C6:{10,3}5.

It is a 2-fold cover of the hemidodecahedron.

It can be 2-split to give S5:{10,3}.

It can be rectified to give the icosidodecahedron.

It is the result of pyritifying (type 3/3/5/3) the tetrahedron.
It is the result of pyritifying (type 4/3/5/3) the cube.

It can be stellated (with path <1>) to give the dodecahedron . The density of the stellation is 7.
It can be stellated (with path <1,-1>) to give the tetrahedron . The multiplicity of the stellation is 5 and the total density is 5.
It can be derived by stellation (with path <1>) from the dodecahedron. The density of the stellation is 7.

Underlying Graph

Its skeleton is dodecahedron.

This is one of the five "Platonic solids".

Cayley Graphs based in this Regular Map

Type II A5

Type III A5×C2

Other Regular Maps

General Index 