Demipenteract

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Demipenteract 5-demicube
Vertex-Edge graph.
Type	Uniform 5-polytope
Families	demihypercube and Semiregular E-polytope
4-faces	26: 10 16-cells 16 5-cells
Cells	120: 40+80 {3,3}
Faces	160 {3}
Edges	80
Vertices	16
Vertex figure	rectified 5-cell
Schläfli symbol	{31,1,2} h{4,3,3,3}
Coxeter-Dynkin diagram
Symmetry group	B5, [3,3,3,4]
Dual	?
Properties	convex

A demipenteract is a name for a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices deleted. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.

It was discovered by Thorold Gosset. Since it was the only semiregular 5-polytope (made of more than one type of regular hypercell), he called it a 5-ic semi-regular.

It can also be called the E5 polytope, in the semiregular E-polytope family with the E6, E7, and E8 polytopes.

Coxeter named this polytope as 1₂₁ from its Coxeter-Dynkin diagram, which has branches of length 2, 1 and 1 with a ringed node on one of the short branches.

Contents 1 Cartesian coordinates 2 See also 3 References 4 External links

[edit] Cartesian coordinates

Cartesian coordinates for the vertices of a demipenteract centered at the origin and edge length 2*sqrt(2) are alternate halves of the penteract:

(±1,±1,±1,±1,±1)

[edit] See also

• 5-polytope

[edit] References

• T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900

[edit] External links

• Olshevsky, George, Demipenteract at Glossary for Hyperspace.
• Multi-dimensional Glossary