5-simplex
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In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos−1(), or approximately 78.46°.
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Article
11 sectionsContents
- Alternate names
- As a configuration
- Regular hexateron cartesian coordinates
- Projected images
- Lower symmetry forms
- Compound
- Related uniform 5-polytopes
- See also
- Notes
- References
- External links
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos−1(), or approximately 78.46°.
The 5-simplex is a solution to the problem: Make 20 equilateral triangles using 15 matchsticks, where each side of every triangle is exactly one matchstick.
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face
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Harold Scott MacDonald Coxeter
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pentachoron
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Coxeter group
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Coxeter–Dynkin diagram
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facet
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geometry
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triangle
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International Standard Book Number
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square
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cube
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digital object identifier
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pentagon
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dimension
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hexagon
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equilateral triangle
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tetrahedron
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Cartesian coordinate system
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vertex
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octahedron
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