❴4,6∣3❵

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{4,6∣3}
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol{4,6∣3}
Elements
Faces30 squares
Edges60
Vertices20
Vertex figureSkew hexagon, edge length
Petrie polygons12 Decagonal-decagrammic coils
HolesTriangles
Measures (edge length 1)
Circumradius1
Related polytopes
ArmySpid
RegimentSpid
Dual{6,4∣3}
Petrie dual{10,6}4,3
φ 2 Tetrahedron
Convex hullSmall prismatodecachoron
Abstract & topological properties
Flag count240
Euler characteristic-10
Schläfli type{4,6}
OrientableYes
Genus6
Properties
SymmetryA4×2, order 240
ConvexNo
Dimension vector(3,2,3)

{4,6∣3} is a regular skew polyhedron in 4-space. Its faces are precisely the square faces of the small prismatodecachoron.

Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the small prismatodecachoron.

Related polytopes[edit | edit source]

{4,6∣3} is the smallest of several skew polyhedra of the form {4,6∣n}, and the only finite case.

External links[edit | edit source]