The compound of six tetrahedra with rotational freedom is a uniform polyhedron compound made of a symmetric arrangement of 6 tetrahedra, considered as antiprisms. It can be constructed by superimposing six tetrahedra within a cube, and then rotating them in pairs about the three axes that pass through the centres of two opposite cubic faces. Each tetrahedron is rotated by an equal (and opposite, within a pair) angle θ. Equivalently, a tetrahedron may be inscribed within each cube in the compound of six cubes with rotational freedom, in such a way as to preserve tetrahedral symmetry.
When θ = 0, all six tetrahedra coincide. When θ is 45 degrees, the more symmetric compound of six tetrahedra (without rotational freedom) arises.
Galleryedit
Compounds of six tetrahedra with rotational freedom
Tetrahedron.stl θ = 0°
Compound of six tetrahedra with rotational freedom (5°).stl θ = 5°
Compound of six tetrahedra with rotational freedom (10°).stl θ = 10°
Compound of six tetrahedra with rotational freedom (15°).stl θ = 15°
Compound of six tetrahedra with rotational freedom (20°).stl θ = 20°
Compound of six tetrahedra with rotational freedom (25°).stl θ = 25°
Compound of six tetrahedra with rotational freedom (30°).stl θ = 30°
Compound of six tetrahedra with rotational freedom (35°).stl θ = 35°
Compound of six tetrahedra with rotational freedom (40°).stl θ = 40°
Compound of six tetrahedra.stl θ = 45°
Referencesedit
Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (03): 447–457, doi:10.1017/S0305004100052440, MR 0397554.
This polyhedron-related article is a stub. You can help Wikipedia by expanding it.
compound, tetrahedra, with, rotational, freedom, type, uniform, compound, index, polyhedra, tetrahedra, faces, triangles, edges, vertices, symmetry, group, tetrahedral, subgroup, restricting, constituent, fold, improper, rotation, compound, tetrahedra, with, r. Compound of six tetrahedra with rotational freedom Type Uniform compound Index UC1 Polyhedra 6 tetrahedra Faces 24 triangles Edges 36 Vertices 24 Symmetry group tetrahedral Td Subgroup restricting to one constituent 4 fold improper rotation S4 The compound of six tetrahedra with rotational freedom is a uniform polyhedron compound made of a symmetric arrangement of 6 tetrahedra considered as antiprisms It can be constructed by superimposing six tetrahedra within a cube and then rotating them in pairs about the three axes that pass through the centres of two opposite cubic faces Each tetrahedron is rotated by an equal and opposite within a pair angle 8 Equivalently a tetrahedron may be inscribed within each cube in the compound of six cubes with rotational freedom in such a way as to preserve tetrahedral symmetry When 8 0 all six tetrahedra coincide When 8 is 45 degrees the more symmetric compound of six tetrahedra without rotational freedom arises Gallery editCompounds of six tetrahedra with rotational freedom nbsp Tetrahedron stl 8 0 nbsp Compound of six tetrahedra with rotational freedom 5 stl 8 5 nbsp Compound of six tetrahedra with rotational freedom 10 stl 8 10 nbsp Compound of six tetrahedra with rotational freedom 15 stl 8 15 nbsp Compound of six tetrahedra with rotational freedom 20 stl 8 20 nbsp Compound of six tetrahedra with rotational freedom 25 stl 8 25 nbsp Compound of six tetrahedra with rotational freedom 30 stl 8 30 nbsp Compound of six tetrahedra with rotational freedom 35 stl 8 35 nbsp Compound of six tetrahedra with rotational freedom 40 stl 8 40 nbsp Compound of six tetrahedra stl 8 45 References editSkilling John 1976 Uniform Compounds of Uniform Polyhedra Mathematical Proceedings of the Cambridge Philosophical Society 79 03 447 457 doi 10 1017 S0305004100052440 MR 0397554 nbsp This polyhedron related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Compound of six tetrahedra with rotational freedom amp oldid 1144772779, wikipedia, wiki, book, books, library,
