❴4,12∣3❵

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{4,12∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{4,12∣3}
Elements
Faces3N  squares
Edges6N 
VerticesN 
Vertex figureSkew dodecagon, edge length
HolesTriangles
Related polytopes
ArmySpidditrah
RegimentSpidditrah
Dual{12,4∣3}
φ 2 Triangular tiling
Convex hullSmall prismated triangular tiling honeycomb
Abstract & topological properties
Flag count24N 
Schläfli type{4,12}
OrientableYes
Genus
Properties
Symmetry[[3,6,3]]
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {4,12∣3} is a paracompact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the square faces of the small prismated triangular 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