Tetrahedron 6-Compound
A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained by arranging six regular tetrahedra about a common C_2 copies. A third can be obtained by combining two oppositely-oriented tetrahedron 3-compounds.
These tetrahedron 6-compounds are illustrated above together with their duals and common midspheres.
The common solids and convex hulls are illustrated above. For the first compound, the interior has the connectivity of a tetrakis hexahedron and the convex hull has the connectivity of the truncated octahedron. For the second, the interior is a 12-dipyramid and the convex hull is a (non-equilateral) 12-prism. For the third, the interior is a truncated 9-trapezohedron (with the connectivity of the (18,2)-generalized Petersen graph) and the convex hull is a gyroelongated 9-dipyramid.
A net for the hull of the first compound is illustrated above, with
See also
Polyhedron Compound, Regular TetrahedronExplore with Wolfram|Alpha
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References
Hart, G. "Uniform Compounds of Uniform Polyhedra." https://www.georgehart.com/virtual-polyhedra/uniform-compounds-info.html.Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant, p. 129, 2002.Skilling, J. "Uniform Compounds of Uniform Polyhedra." Math. Proc. Cambridge Phil. Soc. 79, 447-457, 1976.Referenced on Wolfram|Alpha
Tetrahedron 6-CompoundCite this as:
Weisstein, Eric W. "Tetrahedron 6-Compound." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Tetrahedron6-Compound.html