# Muicosahedron

Muicosahedron
Rank3
SpaceHyperbolic
Notation
Schläfli symbol${\displaystyle \{6,4\mid 5\}}$
Elements
Faces${\displaystyle 2N}$ Hexagons
Edges${\displaystyle 6N}$
Vertices${\displaystyle 3N}$
Vertex figureSkew square, edge length ${\displaystyle \sqrt{3}}$
Related polytopes
ArmyBitped
RegimentBitped
Abstract properties
Schläfli type{6,4}
Topological properties
OrientableYes
Genus
Properties
ConvexNo

The muicosahedron is a regular skew apeirohedron in 3-dimensional hyperbolic space.

The muicosahedron can be constructed from the bitruncated order-5 dodecahedral honeycomb. Its faces are the hexagonal faces of the bitruncated order-5 dodecahedral honeycomb. The pentagonal faces form holes in the muicosahedron.

It can also be constructed from order-5 hexagonal tiling by identifying faces as to make pentagonal holes.

## Vertex coordinates

It's vertex coordinates are the same as the bitruncated order-5 dodecahedral honeycomb.