Tetrahedral bipyramid

{{Short description|Four-dimensional shape}}

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bgcolor=#e7dcc3 colspan=2|Tetrahedral bipyramid
align=center colspan=2|250px Orthogonal projection. 4 red vertices and 6 blue edges make central tetrahedron. 2 yellow vertices are bipyramid apexes.
bgcolor=#e7dcc3|Type |Polyhedral bipyramid
bgcolor=#e7dcc3|Schläfli symbol | {3,3} + { } dt{2,3,3}
bgcolor=#e7dcc3|Coxeter diagram |{{CDD|node_f1|2x|node_f1|3|node|3|node}}
bgcolor=#e7dcc3|Cells |8 {3,3} 30px (4+4)
bgcolor=#e7dcc3|Faces |16 {3} (4+6+6)
bgcolor=#e7dcc3|Edges |14 (6+4+4)
bgcolor=#e7dcc3|Vertices |6 (4+2)
bgcolor=#e7dcc3|Dual |Tetrahedral prism
bgcolor=#e7dcc3|Symmetry group |[2,3,3], order 48
bgcolor=#e7dcc3|Properties |colspan=2|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.https://www.bendwavy.org/klitzing/incmats/tedpy.htm A tetrahedral bipyramid can be seen as two tetrahedral pyramids augmented together at their base.

It is the dual of a tetrahedral prism, {{CDD|node_1|2|node_1|3|node|3|node}}, so it can also be given a Coxeter-Dynkin diagram, {{CDD|node_f1|2x|node_f1|3|node|3|node}}, 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.