Tetrahedral bipyramid explained

bgcolor=#e7dcc3 colspan=2	Tetrahedral bipyramid
align=center colspan=2	Orthogonal projection. 4 red vertices and 6 blue edges make central tetrahedron. 2 yellow vertices are bipyramid apexes.
Type	Polyhedral bipyramid
Schläfli symbol	+ dt
Coxeter diagram
Cells	8 (4+4)
Faces	16 (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, + . 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,, so it can also be given a Coxeter-Dynkin diagram,, 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

• Triangular bipyramid - A lower dimensional analogy of the tetrahedral bipyramid.
• Octahedral bipyramid - A lower symmetry form of the as 16-cell.
• Cubic bipyramid
• Dodecahedral bipyramid
• Icosahedral bipyramid

Notes and References

1. https://www.bendwavy.org/klitzing/incmats/tedpy.htm