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The symmetry groups of the Platonic solids are a special class of three-dimensional point groups known as polyhedral groups. The high degree of symmetry of the Platonic solids can be interpreted in a number of ways. Most importantly, the vertices of each solid are all equivalent under the action of the symmetry group, as are the edges and faces.
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.
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.
They lie in just three symmetry groups, which are named after the Platonic solids: Tetrahedral; Octahedral (or cubic) Icosahedral (or dodecahedral) Any shapes with icosahedral or octahedral symmetry will also contain tetrahedral symmetry.
A comparison between the five platonic solids and the corresponding three platonic hydrocarbons. In organic chemistry, a Platonic hydrocarbon is a hydrocarbon whose structure matches one of the five Platonic solids, with carbon atoms replacing its vertices, carbon–carbon bonds replacing its edges, and hydrogen atoms as needed. [1] [page needed]
In geometry, an octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Regular octahedra occur in nature as crystal structures.
Toggle Solids with full icosahedral symmetry subsection. 1.1 Platonic solids. ... Platonic solids - regular polyhedra (all faces of the same type) {5,3} {3,5}
Of the eight convex deltahedra, three are Platonic solids and five are Johnson solids. They are: [2] regular tetrahedron, a pyramid with four equilateral triangles, one of which can be considered the base. triangular bipyramid, regular octahedron, and pentagonal bipyramid, a bipyramid with six, eight, and ten equilateral triangles, respectively ...