The hemidodecahedron

Statistics

genus ^c	1, non-orientable
Schläfli formula ^c	{5,3}
V / F / E ^c	10 / 6 / 15
notes
vertex, face multiplicity ^c	1, 1
Petrie polygons	6, each with 5 edges
antipodal sets	6 of ( f, p1 ), 5 of ( 3e )
rotational symmetry group	A5, with 60 elements
full symmetry group	A5, with 60 elements
its presentation ^c	< r, s, t \| r², s², t², (rs)⁵, (st)³, (rt)², (srsrst)² >
C&D number ^c	N1.2′
The statistics marked ^c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the hemi-icosahedron.

It is self-Petrie dual.

It can be 2-fold covered to give the dodecahedron.

It can be 2-split to give N6:{10,3}₁₀.

It can be rectified to give the hemi-icosidodecahedron.

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

List of regular maps in non-orientable genus 1.

Underlying Graph

Its skeleton is Petersen graph.

Comments

If you take hemi-dodecahedra and glue them together five to an edge, you will find that 57 of them form a regular polytope, the 57-cell, Schläfli symbol {5,3,5} (do not try this at home – it is not possible while you are embedded in 3-space). Its rotational symmetry group is PSL(2,19).

Other Regular Maps

General Index