The tetrahedron

Statistics

genus c0, orientable
Schläfli formula c{3,3}
V / F / E c 4 / 4 / 6
notesreplete singular is a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
3, each with 4 edges
antipodal sets4 of ( v, f ), 3 of ( 2e, p1 )
rotational symmetry groupA4, with 12 elements
full symmetry groupS4, with 24 elements
its presentation c< r, s, t | r2, s2, t2, (rs)3, (st)3, (rt)2 >
C&D number cR0.1
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 the hemicube.

It can be 2-split to give {6,3}(2,2).

It can be rectified to give the octahedron.

It is the diagonalisation of the di-square.

It can be pyritified (type 3/3/5/3) to give the dodecahedron.

Its full shuriken is C4:{6,4}3.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is K4.

Comments

This is one of the five "Platonic solids".

Cayley Graphs based in this Regular Map


Type I

C2×C2

Type II

A4

Type III

S4

Other Regular Maps

General Index

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