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Platonic solid. In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
Polyhedron. In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set.
The five Platonic solids have an Euler characteristic of 2. This simply reflects that the surface is a topological 2-sphere, and so is also true, for example, of any polyhedron which is star-shaped with respect to some interior point.
The Johnson solids are named after American mathematician Norman Johnson(1930–2017), who published a list of 92 such polyhedra in 1966. His conjecture that the list was complete and no other examples existed was proven by Russian-Israeli mathematician Victor Zalgaller(1920–2020) in 1969.
List of states of matter. Matter organizes into various phases or states of matter depending on its constituents and external factors like pressure and temperature. In common temperatures and pressures, atoms form the three classical states of matter: solid, liquid and gas. Complex molecules can also form various mesophases such as liquid ...
A well-studied example is the radical ion salt TTF-TCNQ with a conductivity of 5 x 10 2 Ω −1 cm −1, [5] much closer to copper (ρ = 6 x 10 5 Ω −1 cm −1) [8] than many molecular solids. [ 31 ] [ 18 ] [ 30 ] The coulombic interaction in TTF-TCNQ stems from the large partial negative charge (δ = -0.59) on the cyano- moiety on TCNQ at ...
A regular dodecahedron or pentagonal dodecahedron 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, including ...
A crystal is a solid where the atoms form a periodic arrangement. (Quasicrystalsare an exception, see below). Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a polycrystallinestructure.