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The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. Polytope elements [ edit ]
The following table contains the 92 Johnson solids, with edge length . The table includes the solid's enumeration (denoted as ). [7] It also includes the number of vertices, edges, and faces of each solid, as well as its symmetry group, surface area , and volume .
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek -derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a strictly convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two solids with such a property: the first solids are the pyramids, cupolas. and a rotunda; some of the solids may be ...
Rhombicuboctahedron and pseudo-rhombicuboctahedron. In geometry, an Archimedean solid is one of 13 convex polyhedra whose faces are regular polygons and whose vertices are all symmetric to each other. They were first enumerated by Archimedes. They belong to the class of convex uniform polyhedra, the convex polyhedra with regular faces and ...
Hexagon. In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. [1] The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual . There are three elongated pyramids that are Johnson solids: Elongated triangular pyramid ( J7 ), Elongated square pyramid ( J8 ), and.
The surface area of an elongated triangular cupola is the sum of all polygonal face's area. The volume of an elongated triangular cupola can be ascertained by dissecting it into a cupola and a hexagonal prism, after which summing their volume. Given the edge length , its surface and volume can be formulated as: [2] It has the three-dimensional ...
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