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In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape is also called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron.
The same shape is also known as a triangular dipyramid [1] [2] or trigonal bipyramid. [3] If these tetrahedra are regular, all faces of a triangular bipyramid are equilateral. It is an example of a deltahedron, composite polyhedron, and Johnson solid. Many polyhedra are related to the triangular bipyramid, such as similar shapes derived from ...
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
A wedge-shaped crystal form of the tetragonal or orthorhombic system. It has four triangular faces that are alike and that correspond in position to alternate faces of the tetragonal or orthorhombic dipyramid. It is symmetrical about each of three mutually perpendicular diad axes of symmetry in all classes except the tetragonal-disphenoidal, in ...
The deltahedron is named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ. [1] The deltahedron can be categorized by the property of convexity . There are eight convex deltahedra, which can be used in the applications of chemistry as in the polyhedral skeletal electron pair theory and chemical compounds .
The kaleidocycle has an additional property that it can be continuously twisted around a ring axis, showing 4 sets of 6 triangular faces. The kaleidocycle is invariant under twists about its ring axis by k π / 2 {\displaystyle k\pi /2} , where k {\displaystyle k} is an integer, and can therefore be continuously twisted.
"You could see a diamond-shaped face, and someone else would call it an oblong face," says Dr. Tripathi. "There's a more gaunt temple area, more width to the mid-face, and then a narrower lower face."
Slicing a rhombic dodecahedron in half through the long diagonals of four of its faces results in a self-dual enneahedron, the square diminished trapezohedron, with one large square face, four rhombus faces, and four isosceles triangle faces. Like the rhombic dodecahedron itself, this shape can be used to tessellate three-dimensional space. [6]