Tetrahedral bipyramidOrthogonal projection.4 red vertices and 6 blue edges make central tetrahedron. 2 yellow vertices are bipyramid apexes.TypePolyhedral bipyramidSchläfli symbol {3,3} + { }dt{2,3,3}Coxeter diagramCells8 {3,3} (4+4)Faces16 {3} (4+6+6)Edges14 (6+4+4)Vertices6 (4+2)DualTetrahedral prismSymmetry group[2,3,3], order 48Propertiesconvex, regular-faced, Blind polytope, projectively unique 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, , 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
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