Tetrahedral bipyramid

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Tetrahedral bipyramid
Tetrahedral bipyramid-ortho.png
Orthogonal projection.
4 red vertices and 6 blue edges make central tetrahedron. 2 yellow vertices are bipyramid apexes.
Type Polyhedral bipyramid
Schläfli symbol {3,3} + { }
dt{2,3,3}
Coxeter diagram CDel node f1.pngCDel 2x.pngCDel node f1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Cells 8 {3,3} Tetrahedron.png (4+4)
Faces 16 {3} (4+6+6)
Edges 14 (6+4+4)
Vertices 6 (4+2)
Dual Tetrahedral prism
Symmetry group [2,3,3], order 48
Properties convex, regular-faced, Blind polytope

In 4-dimensional geometry, the tetrahedral bipyramid is the direct sum of a tetrahedron and a segment, {3,3} + { }. Each face of a central tetrahedron is attached with two tetrahedra, creating 8 tetrahedral cells, 16 triangular faces, 14 edges, and 6 vertices.[1] A tetrahedral bipyramid can be seen as two tetrahedral pyramids augmented together at their base.

It is the dual of a tetrahedral prism, CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png, so it can also be given a Coxeter-Dynkin diagram, CDel node f1.pngCDel 2x.pngCDel node f1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png, and both have Coxeter notation symmetry [2,3,3], order 48.

Being convex with all regular cells (tetrahedra) means that it is a Blind polytope.

This bipyramid exists as the cells of the dual of the uniform rectified 5-simplex, and rectified 5-cube or the dual of any uniform 5-polytope with a tetrahedral prism vertex figure. And, as well, it exists as the cells of the dual to the rectified 24-cell honeycomb.

See also

References