❴4,10∣3❵

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{4,10∣3}
Rank3
Dimension3
TypeRegular
SpaceHyperbolic
Notation
Schläfli symbol{4,10∣3}
Elements
Faces5N  squares
Edges10N 
Vertices2N 
Vertex figureSkew decagon, edge length
HolesTriangles
Measures (edge length 1)
Circumradius
Related polytopes
ArmySpih
RegimentSpih
Dual{10,4∣3}
φ 2 Icosahedron
φ 3 {10,10/3∣5}
φ 4 Great dodecahedron
Convex hullSmall prismatoicosahedral honeycomb
Abstract & topological properties
Flag count40N 
Schläfli type{4,10}
OrientableYes
Genus
Properties
Symmetry[[3,5,3]]
ConvexNo
Dimension vector(2,1,2)
History
Discovered byCyril Garner
First discovered1967

The {4,10∣3} is a compact regular skew apeirohedron in 3-dimensional hyperbolic space. Its faces are precisely the square faces of the small prismatoicosahedral 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