❴❴3,4❵,❴4,4∣4❵❵

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{{3,4},{4,4∣4}}
Rank4
Dimension4
TypeRegular
Notation
Schläfli symbol
  • {{3,4},{4,4∣4}}
Elements
Cellsoctahedra
Facestriangles
Edges
Vertices
Vertex figureSquare duocomb
Related polytopes
ArmyIcot
RegimentIcot
Dual{{4,4∣4},{4,3}}
Convex hull24-cell honeycomb
Abstract & topological properties
Flag count
Schläfli type{3,4,4}
OrientableYes
Properties
Flag orbits1
ConvexNo
Dimension vector(3,3,2,3)

{{3,4},{4,4∣4}} is a regular skew apeirochoron in 4-dimensional Euclidean space.

It is universal and locally toroidal.

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the 24-cell honeycomb.

Related polytopes[edit | edit source]

3 {{3,4},{4,4∣4}} form the facets of the Petrial 24-cell honeycomb.

Bibliography[edit | edit source]

  • McMullen, Peter (2009), "Regular Apeirotopes of Dimension and Rank 4" (PDF), Discrete computational geometry, 42, doi:10.1007/s00454-009-9186-y