The 12-hosohedron

Statistics

genus c0, orientable
Schläfli formula c{2,12}
V / F / E c 2 / 12 / 12
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c12, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4th-order Petrie polygons
5th-order holes
5th-order Petrie polygons
6th-order holes
2, each with 12 edges
12, each with 2 edges
4, each with 6 edges
12, each with 2 edges
6, each with 4 edges
12, each with 2 edges
4, each with 6 edges
12, each with 2 edges
2, each with 12 edges
12, each with 2 edges
antipodal sets1 of ( 2v ), 6 of ( 2f, 2h3, 2h5; 2p3 ), 6 of ( 2e, 2h2, 2h4, 2h6 ), 2 of ( 2p2, 2p4 )
rotational symmetry groupD24, with 24 elements
full symmetry groupD24×C2, with 48 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)12, (rt)2 >
C&D number cR0.n12
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the di-dodecagon.

Its Petrie dual is S5:{12,12}.

It is a 2-fold cover of the hemi-12-hosohedron.

It can be rectified to give the 12-lucanicohedron.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 12 . K2.

Cayley Graphs based in this Regular Map


Type II

D24

Type IIa

C12×C2

Other Regular Maps

General Index

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