The 3-hosohedron

Statistics

genus c0, orientable
Schläfli formula c{2,3}
V / F / E c 2 / 3 / 3
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 1
Petrie polygons
1, with 6 edges
antipodal sets1 of ( 2v ), 3 of ( f, e )
rotational symmetry groupD6, with 6 elements
full symmetry groupD12, with 12 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)3, (rt)2 >
C&D number cR0.n3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the di-triangle.

Its Petrie dual is {6,3}(1,1).

It can be rectified to give the 3-lucanicohedron.

It can be Eppstein tunnelled to give {6,3}(0,2).

It can be obtained by truncating the dimonogon.

It can be pyritified (type 2/3/4/3) to give the cube.

Its half shuriken is the hemi-6-hosohedron.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 3 . K2.

Cayley Graphs based in this Regular Map


Type II

D6

Type IIa

C6

Type III

D12

Type IIIa

D12

Other Regular Maps

General Index

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