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The concave equilateral dodecahedron, called an endo-dodecahedron. [clarification needed] A cube can be divided into a pyritohedron by bisecting all the edges, and faces in alternate directions. A regular dodecahedron is an intermediate case with equal edge lengths. A rhombic dodecahedron is a degenerate case with the 6 crossedges reduced to ...
It has 28 faces: twelve regular pentagons arranged in four panels of three pentagons each, four equilateral triangles (shown in blue), and six pairs of isosceles triangles (shown in yellow). All edges of the tetrated dodecahedron have the same length, except for the shared bases of these isosceles triangles, which are approximately 1.07 times ...
A topological icosidodecahedron in truncated cube, inserting 6 vertices in center of octagons, and dissecting them into 2 pentagons and 2 triangles. The truncated cube can be turned into an icosidodecahedron by dividing the octagons into two pentagons and two triangles. It has pyritohedral symmetry.
3D model of a elongated dodecahedron. In geometry, the elongated dodecahedron, [1] extended rhombic dodecahedron, rhombo-hexagonal dodecahedron [2] or hexarhombic dodecahedron [3] is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi.
In this construction, all the faces are computed to be the same distance from the center. 80 of the triangles are equilateral, and 60 triangles from the pentagons are isosceles. It is a (2,1) geodesic polyhedron, made of all triangles. The path between the valence-5 vertices is two edges in a row, and then a turn and one more edge.
In geometry, a tetrahedrally diminished [a] dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron [1]) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals). [2]
A polyhedron with only equilateral triangles as faces is called a deltahedron. There are only eight different convex deltahedra, one of which is the gyroelongated square bipyramid. [ 5 ] More generally, the convex polyhedron in which all faces are regular is the Johnson solid , and every convex deltahedron is a Johnson solid.
The dihedral angle of an elongated square bipyramid between two adjacent triangles is the dihedral angle of an equilateral triangle between its lateral faces, (/) The dihedral angle of an elongated square bipyramid between two adjacent squares is the dihedral angle of a cube between those, π / 2 {\displaystyle \pi /2}