S4:{5,5}

Statistics

genus c4, orientable
Schläfli formula c{5,5}
V / F / E c 12 / 12 / 30
notesreplete singular is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
10, each with 6 edges
20, each with 3 edges
6, each with 10 edges
antipodal sets6 of ( 2v, 2f, p2 ), 15 of ( 2e )
rotational symmetry groupA5, with 60 elements
full symmetry group120 elements.
its presentation c< r, s, t | t2, (rs)2, (rt)2, (st)2, r‑5, (s‑1r)3 >
C&D number cR4.6
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

Its Petrie dual is N10.5′.

It is a 2-fold cover of C5:{5,5}.

It can be 2-split to give R13.8′.

It can be rectified to give S4:{5,4}.

It can be derived by stellation (with path <>/2) from the icosahedron. The density of the stellation is 3.
It can be derived by stellation (with path <1/-1>) from the icosahedron. The density of the stellation is 3.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is icosahedron.

Comments

This is the small stellated dodecahedron, embedded in the surface where it is at home, instead of painfully immersed in ℝ3. It is also the great dodecahedron, likewise.


Other Regular Maps

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The images on this page are copyright © 2010 N. Wedd