❴4,6∣6❵

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{4,6∣6}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Coxeter diagramx4o6o|x6o
Schläfli symbol{4,6∣6}
Elements
Faces6N  Squares
Edges12N 
Vertices4N 
Vertex figureSkew hexagon, edge length
HolesHexagons
Related polytopes
ArmySpiddihexah
RegimentSpiddihexah
Dual{6,4∣6}
φ 2 Hexagonal tiling
Convex hullSmall prismated order-6 hexagonal tiling honeycomb
Abstract & topological properties
Flag count48N 
Schläfli type{4,6}
OrientableYes
Genus
Properties
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

{4,6∣6} is a paracompact regular skew polyhedron in 3-dimensional hyperbolic space. Its faces are exactly the square faces of the small prismated order-6 hexagonal tiling honeycomb.

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the small prismated order-6 hexagonal tiling honeycomb.

Related polytopes[edit | edit source]

{4,6∣5} is one of several skew polyhedra of the form {4,6∣n}.

There is a direct correspondence between these and the regular polyhedra with triangular vertex figures.

Each of the latter appears as a pseudocell of the corresponding former. This is a part of a general correspondence where {n,p} appears as a pseudocell of {4,2pn}.

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