The 3-hosohedron


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


Type IIa


Type III


Type IIIa


Other Regular Maps

General Index

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