The hemidodecahedron


genus c1, non-orientable
Schläfli formula c{5,3}
V / F / E c 10 / 6 / 15
notesreplete singular is a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
6, each with 5 edges
antipodal sets6 of ( f, p1 ), 5 of ( 3e )
rotational symmetry groupA5, with 60 elements
full symmetry groupA5, with 60 elements
its presentation c< r, s, t | r2, s2, t2, (rs)5, (st)3, (rt)2, (srsrst)2 >
C&D number cN1.2′
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 C6:{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.


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

The image on this page is copyright © 2010 N. Wedd