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 N6:{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.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is dodecahedron.

Comments

This is one of the five "Platonic solids".

Cayley Graphs based in this Regular Map

Type II

Type III

A5×C2

Other Regular Maps

General Index