
genus ^{c}  1, nonorientable 
Schläfli formula ^{c}  {5,3} 
V / F / E ^{c}  10 / 6 / 15 
notes  
vertex, face multiplicity ^{c}  1, 1 
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  r^{2}, s^{2}, t^{2}, (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. 
Its dual is
It is selfPetrie dual.
It can be 2fold covered to give
It can be 2split to give
It can be rectified to give
It is the result of pyritifying (type 4/3/5/3)
List of regular maps in nonorientable genus 1.
Its skeleton is Petersen graph.
If you take hemidodecahedra and glue them together five to an edge, you will find that 57 of them form a regular polytope, the 57cell, Schläfli symbol {5,3,5} (do not try this at home – it is not possible while you are embedded in 3space). Its rotational symmetry group is PSL(2,19).
Orientable  
Nonorientable 
The image on this page is copyright © 2010 N. Wedd