

genus ^{c}  4, orientable 
Schläfli formula ^{c}  {5,5} 
V / F / E ^{c}  12 / 12 / 30 
notes  
vertex, face multiplicity ^{c}  1, 1 
10, each with 6 edges 20, each with 3 edges 6, each with 10 edges  
antipodal sets  6 of ( 2v, 2f, p2 ), 15 of ( 2e ) 
rotational symmetry group  A5, with 60 elements 
full symmetry group  120 elements. 
its presentation ^{c}  < r, s, t  t^{2}, (rs)^{2}, (rt)^{2}, (st)^{2}, r^{‑5}, (s^{‑1}r)^{3} > 
C&D number ^{c}  R4.6 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
It is selfdual.
Its Petrie dual is
It is a 2fold cover of
It can be 2split to give
It can be rectified to give
Its 2hole derivative is
It can be derived by stellation (with path <>/2) from
It can be derived by stellation (with path <1/1>) from
List of regular maps in orientable genus 4.
Its skeleton is icosahedron.
This is the small stellated dodecahedron, embedded in the surface where it is at home, instead of painfully immersed in ℝ^{3}. It is also the great dodecahedron, likewise.
Orientable  
Nonorientable 
The images on this page are copyright © 2010 N. Wedd