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In pyritohedral pyrite, the faces have a Miller index of (210), which means that the dihedral angle is 2·arctan(2) ≈ 126.87° and each pentagonal face has one angle of approximately 121.6° in between two angles of approximately 106.6° and opposite two angles of approximately 102.6°. The following formulas show the measurements for the ...
A regular dodecahedron or pentagonal dodecahedron [notes 1] is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron ...
Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex)
This is left blank for non-orientable polyhedra and hemipolyhedra (polyhedra with faces passing through their centers), for which the density is not well-defined. Note on Vertex figure images: The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations.
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.
The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24-cell's octahedral cells. The remaining 12 octahedral cells project onto the faces of the rhombic dodecahedron.
An example is the rhombicuboctahedron, constructed by separating the cube or octahedron's faces from the centroid and filling them with squares. [8] Snub is a construction process of polyhedra by separating the polyhedron faces, twisting their faces in certain angles, and filling them up with equilateral triangles.
The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is internal to its dual, the small stellated dodecahedron. This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} " decagram "); this series continues into the fourth ...