# Regular Polyhedra on the Genus-C4 non-Orientable Manifold

This page shows some of the regular maps that can be drawn on the genus-4c (a sphere plus four crosscaps) non-orientable manifold. For the purpose of these pages, a "regular map" is defined here.

To draw these maps, we need a way of portraying this surface in 2-space. Pink letters show how the "cut edges" are to be joined up, and light pink regions are not part of the surface. This is further explained by the page Representation of 2-manifolds.

Schläfli
symbol
C&D no.
V+F-E=Euthumbnail
dual

Petrie dual

Symmetry
Group
{6,4}3
N4.2′
6+4-12=-2 next

S1{3,6}(2,2)

[48] 2
{4,6}3
N4.2
6+4-12=-2 prec.

octahedron

{6,4}6
N4.1′
6+4-12=-4 next

self

[48]

cantankerous

2
{4,6}6
R4.1
4+6-12=-4 prec.

The things listed below are not regular maps.

 {18,3} 6+1-9=-2 {3,18} D6 ∄ See {3,18} for an unconvincing proof. {3,18} 1+6-9=-2 {18,3}The triangular prism {8,3} 16+6-24=-2 {3,8} {3,8} 61+6-24=-2 {8,3}

Index to other pages on regular maps;
indexes to those on S0 C1 S1 S2 C4 C5 S3 C6 S4.
Some pages on groups