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The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices ...
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.
In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron [1] is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.
The intersection of both solids is the icosidodecahedron, and their convex hull is the rhombic triacontahedron. Seen from 2-fold, 3-fold and 5-fold symmetry axes The decagon on the right is the Petrie polygon of both solids.
Important classes of convex polyhedra include the family of prismatoid, the Platonic solids, the Archimedean solids and their duals the Catalan solids, and the regular polygonal faces polyhedron. The prismatoids are the polyhedron whose vertices lie on two parallel planes and their faces are likely to be trapezoids and triangles. [ 18 ]
Truncated icosahedron, one of the Archimedean solids illustrated in De quinque corporibus regularibus. The five Platonic solids (the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron) were known to della Francesca through two classical sources: Timaeus, in which Plato theorizes that four of them correspond to the classical elements making up the world (with the fifth, the ...
The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. The regular hexahedron is a cube . Table of polyhedra
Platonic solids (regular convex) Tetrahedron {3,3} (3.3.3) arccos ... 5 / 3 .6)