❴8,4∣4❵

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{8,4∣4}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{8,4∣4}
Elements
Facesoctagons
Edges
Vertices
Vertex figureSkew square, edge length
HolesSquares
Related polytopes
Dual{4,8∣4}
φ 2 Square dihedron
Convex hullBitruncated order-4 square tiling honeycomb
Abstract & topological properties
Schläfli type{8,4}
OrientableYes
Genus
Properties
Symmetry
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {8,4∣4} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the square faces of the bitruncated order-4 square tiling honeycomb.

Bibliography[edit | edit source]

  • Garner, Cyril (1967), "Regular skew polyhedra in hyperbolic three-space" (PDF), Canadian Journal of Mathematics, 19, doi:10.4153/CJM-1967-106-9