Petrial mutetrahedron

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Petrial mutetrahedron
Rank3
Notation
Schläfli symbol
[1]
Elements
Faces triangular helices
Edges
Vertices
Vertex figureSkew hexagon
Petrie polygons hexagons
Related polytopes
ArmyBatatoh
RegimentBatatoh
Petrie dualMutetrahedron
φ 2 Petrial tetrahedron
κ ?Mucube
Abstract & topological properties
Flag count
Schläfli type{∞,6}
Properties
ConvexNo
Dimension vector(1,1,2)
History
Discovered byBranko Grünbaum
First discovered1977

The Petrial mutetrahedron is a regular skew apeirohedron in 3-dimensional Euclidean space. It is the Petrie dual of the mutetrahedron, and it has 6 triangular helices meeting at a vertex.

Vertex coordinates[edit | edit source]

The petrial mutetrahedron's coordinates are the same as those of the cyclotruncated tetrahedral-octahedral honeycomb.

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.