Petrial mucube

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Petrial mucube
Rank3
Notation
Schläfli symbol
[1]
Elements
FacesN  triangular helices
Edges3M×N 
VerticesM×N 
Vertex figureSkew hexagon
Petrie polygonssquares
Related polytopes
ArmyCubic honeycomb
RegimentCubic honeycomb
Petrie dualMucube
φ 2 Petrial cube
κ ?Mutetrahedron
Abstract & topological properties
Flag count12M×N 
Schläfli type{∞,6}
OrientableYes
Properties
ConvexNo
Dimension vector(1,1,2)
History
Discovered byBranko Grünbaum
First discovered1975
A section of the mucube with a Petrie polygon highlighted in red.

The Petrial mucube is a regular skew apeirohedron in 3 dimensional Euclidean space. It is the Petrie dual of the mucube.

Vertex coordinates[edit | edit source]

It's vertex coordinates are the same as the mucube. For a Petrial mucube of unit side length its vertices take on the coordinates

  • ,

where i , j , k  are any three integers.

External links[edit | edit source]

References[edit | edit source]

  1. McMullen & Schulte (1997:465)

Bibliography[edit | edit source]

  • Grünbaum, Branko (1977), "Regular polyhedra - old and new" (PDF), Aequationes Mathematicae, 16, doi:10.1007/BF01836414
  • McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.