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Unlike the tetragonal disphenoid, the rhombic disphenoid has no reflection symmetry, so it is chiral. [8] Both tetragonal disphenoids and rhombic disphenoids are isohedra: as well as being congruent to each other, all of their faces are symmetric to each other. It is not possible to construct a disphenoid with right triangle or obtuse triangle ...
An orientation of the tetragonal disphenoid honeycomb can be obtained by starting with a cubic honeycomb, subdividing it at the planes =, =, and = (i.e. subdividing each cube into path-tetrahedra), then squashing it along the main diagonal until the distance between the points (0, 0, 0) and (1, 1, 1) becomes the same as the distance between the ...
The snub disphenoid can be constructed in different ways. As suggested by the name, the snub disphenoid is constructed from a tetragonal disphenoid by cutting all the edges from its faces, and adding equilateral triangles (the light blue colors in the following image) that are twisted in a certain angle between them.
Regular polyhedron. Platonic solid: . Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot ...
An example of the tetragonal crystals, wulfenite Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system. In crystallography, the tetragonal crystal system is one of the 7 crystal systems.
A space-filling tetrahedral disphenoid inside a cube. Two edges have dihedral angles of 90°, and four edges have dihedral angles of 60°. A disphenoid is a tetrahedron with four congruent triangles as faces; the triangles necessarily have all angles acute. The regular tetrahedron is a special case of a disphenoid.
The convex hull of the truncated 24-cell and its dual (assuming that they are congruent) is a nonuniform polychoron composed of 480 cells: 48 cubes, 144 square antiprisms, 288 tetrahedra (as tetragonal disphenoids), and 384 vertices. Its vertex figure is a hexakis triangular cupola. Vertex figure
Tetragonal disphenoid: Oblate tetrahedrille: Tetragonal disphenoid: J 17 A 18 W 13 G 25 t 0,1,2 δ 4 nc [4,3,4] n-tCO-trille (Cantitruncated cubic honeycomb) Mirrored sphenoid: Triangular pyramidille: Mirrored sphenoid, , J 18 A 19 W 19 G 20 t 0,1,3 δ 4 nc [4,3,4] 1-RCO-trille (Runcitruncated cubic honeycomb) Trapezoidal pyramid: Square ...