The di-square

Statistics

genus c0, orientable
Schläfli formula c{4,2}
V / F / E c 4 / 2 / 4
notesVertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 4
Petrie polygons
2, each with 4 edges
antipodal sets2 of ( 2v, 2e ), 1 of ( 2f )
rotational symmetry groupD8, with 8 elements
full symmetry groupD8×C2, with 16 elements
its presentation c< r, s, t | r2, s2, t2, (rs)4, (st)2, (rt)2 >
C&D number cR0.n4′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the 4-hosohedron.

It is self-Petrie dual.

It is a 2-fold cover of the hemi-di-square.

It can be 3-split to give the di-dodecagon.

It can be rectified to give the 4-lucanicohedron.

It can be diagonalised to give the tetrahedron.

It is a member of series m.

List of regular maps in orientable genus 0.

Wireframe constructions

pd {4,2} 4/1 | 2 | 4 × the 1-hosohedron
qd {4,2} 4/1 | 2 | 4 × the 1-hosohedron
rd {4,2} 4/1 | 2 | 4 × the 1-hosohedron
td {4,2} 4/1 | 2 | 4 × the 1-hosohedron

Underlying Graph

Its skeleton is 4-cycle.

Cayley Graphs based in this Regular Map


Type I

C4

Type II

D8

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |

The image on this page is copyright © 2010 N. Wedd