Топ-100 ★ Free online encyclopedia. Did you know? page 389

★ Free online encyclopedia. Did you know? page 389




                                               

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, which is not homogeneous, and each face is a regular polygon. There is no requirement that each side must be the same polygon, or that the same polygons to unite around each vertex. Ex ...

                                               

Bilunabirotunda

In geometry, bilunabirotunda is one of the solid Johnson. Johnson solids is one of 92 strictly convex polyhedra that consists of a regular polygon faces but are not uniform polyhedra. They were named by Norman Johnson, who first listed these poly ...

                                               

Birotunda

In geometry birotunda any member of the family of dihedral-symmetric polyhedra, formed from two rotunda adjoined to a large face. They are similar to bicupola but instead of alternating squares and triangles, his deputies pentagons and triangles ...

                                               

Diminished rhombicosidodecahedron

In geometry, diminished rhombicosidodecahedron is one of the solid Johnson. It can be constructed as a rhombicosidodecahedron with pentagonal removed the dome. Johnson solids is one of 92 strictly convex polyhedra that consists of a regular polyg ...

                                               

Elongated square gyrobicupola

In geometry, the elongated square gyrobicupola or pseudo-rhombicuboctahedron is one of the solid Johnson. This is usually not an Archimedean solid, although its faces are composed of regular polygons that meet in the same pattern at each of its v ...

                                               

Metagyrate diminished rhombicosidodecahedron

In geometry, metagyrate diminished rhombicosidodecahedron is one of the solid Johnson. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotates by 36 degrees, and not opposing pentagonal cupola removed. Johnson solids ...

                                               

Pentagonal cupola

In geometry, the pentagonal cupola is one of the solid Johnson. It can be obtained as part of a rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 Pentagon, and 1 decagon. Johnson solids is one of 92 s ...

                                               

Pentagonal rotunda

In geometry, the pentagonal rotunda is one of the Johnson solids. This can be seen as half icosidodecahedron, or as half of a pentagonal orthobirotunda. Johnson solids is one of 92 strictly convex polyhedra that consists of a regular polygon face ...

                                               

Rotunda (geometry)

In geometry, a rotunda is any member of the family of dihedral-symmetric polyhedra. They look like a dome, but instead of alternating squares and triangles, his deputies pentagons and triangles around an axis. The pentagonal rotunda is the Johnso ...

                                               

Jessens icosahedron

Jessens icosahedron, sometimes called the Jessens orthogonal icosahedron is a convex polyhedron with the same number of vertices, edges, and faces of an icosahedron. Her face only meet at a right angle, although they may not be parallel to the co ...

                                               

Schonhardt polyhedron

In geometry, Schonhardt polyhedron is the simplest non-convex polyhedron that cannot be triangulated the to the tetrahedra without adding new vertices. It is named after German mathematician Erich Schonhardt, who first described it in 1928.

                                               

Antiprism

In the geometry of N-coal antiprism is a polyhedron composed of two parallel copies of a particular N-sided polygon, connected by an alternating band of triangles. Antiprisms are a subclass of the prismatoids and the type of the snub polyhedron. ...

                                               

Crossed pentagonal cuploid

In geometry, the crossed pentagonal cupoloid or the intersection of the pentagonal semicupola is a member of the infinite family cuploids. It can be obtained as part of the great complex rhombicosidodecahedron. As with all cupolae, the base polyg ...

                                               

Crossed pentagrammic cupola

In geometry, the pentagrammic crossed-dome is one of the nonconvex Johnson solid isomorphic, being topologically identical to the convex pentagonal cupola. It can be obtained as part of the Great rhombicosidodecahedron or quasirhombicosidodecahed ...

                                               

Crossed square cupola

In geometry, the crossed square cupola is one of the nonconvex Johnson solid isomorphic, being topologically identical to the convex square cupola. It can be obtained as part of the nonconvex great rhombicuboctahedron or quasirhombicuboctahedron. ...

                                               

Heptagrammic cupola

In geometry, heptagrammic dome of stars the dome is made from an heptagram, {7 / 3} and parallel tetradecagram, {14 / 3}, 7 mutually intersecting equilateral triangles and squares.

                                               

Octagrammic cupola

In geometry, octagrammic dome of stars the dome is made from an octagram, {8 / 3} and parallel hexadecagram, {16 / 3}, connected by 8 equilateral triangles and squares.

                                               

Pentagrammic cuploid

In geometry, the pentagrammic cuploid or pentagrammmic semicupola is the simplest of an infinite family of cuploids. It can be obtained as part of a small complex rhombicosidodecahedron. As with all cupolae, the base polygon has twice as many edg ...

                                               

Prism (geometry)

In geometry, a prism is a polyhedron containing N-sided polygon base, second base, which is a translated copy of the first, and N other persons to enter the corresponding sides of the two bases. All sections parallel database translations databas ...

                                               

Prismatic uniform polyhedron

In geometry, a prismatic uniform polyhedron uniform polyhedron with dihedral symmetry. They exist in two infinite families of uniform prisms and antiprisms uniform. They all have their tops in parallel planes and therefore prismatoids.

                                               

Pseudo-uniform polyhedron

Pseudo-uniform polyhedron is a polyhedron which has regular polygons as faces and has the same vertex configuration at all vertices but is not vertex-transitive: it is not true that for any two vertices there is symmetry of the polyhedron mapping ...

                                               

Pseudo great rhombicuboctahedron

In geometry, a pseudo great rhombicuboctahedron is one of the two pseudo-uniform polyhedra, the other convex elongated square gyrobicupola or pseudo rhombicuboctahedron. It has the same vertex figure as nonconvex great rhombicuboctahedron, but no ...

                                               

Self-dual polyhedron

                                               

Stellated dodecahedron

                                               

Uniform polyhedron

A uniform polyhedron has regular polygons as faces and is vertex transitive. From this it follows that all vertices coincide. Uniform polyhedra may be regular if also face and edge transitive, quasi-regular, if edge transitive but not face transi ...

                                               

Dodecadodecahedron

In geometry, dodecadodecahedron is a nonconvex uniform polyhedron, indexed as 36. This straightening of the great dodecahedron. It was discovered independently Hess, Badoureau and Pitsch. The edges of this model form 10 Central hexagons, and thes ...

                                               

Great dirhombicosidodecahedron

In geometry, the great dirhombicosidodecahedron is a nonconvex uniform polyhedron, indexed last as 75. It has 124 persons, 240 edges, and 60 vertices. This is the only non-degenerate uniform polyhedron with more than six faces meeting at the vert ...

                                               

Great disnub dirhombidodecahedron

In geometry, the great disnub dirhombidodecahedron, also called Schillings drawing, geek uniform star polyhedron. This was proven in 1970 that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms. John Ski ...

                                               

Great dodecahemidodecahedron

In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as the 70. It has 18 faces, 60 edges, and 30 vertices. His figure vertex is a crossed quadrilateral. In addition to regular small stellate dodecahedron { 5 / ...

                                               

Great snub icosidodecahedron

In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U 57. It has 92 faces and 150 edges, and 60 vertices. It can be represented by a Schlafli symbol of SR{ 5 ⁄ 2.3} and Coxeter-Dynkin diagram. This polyhedr ...

                                               

Hemipolyhedron

In geometry, hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "Hemi" faces lie parallel to the faces of some other symmetrical polyhedron, and their count is half the number of faces of a polyhedron t ...

                                               

List of uniform polyhedra by Schwarz triangle

There are many relations between uniform polyhedra. In the Wythoff construction is able to build almost all forms of polyhedra of acute and obtuse triangles Schwartz. The numbers that can be used for parties not acute or obtuse dihedral Schwarz t ...

                                               

List of uniform polyhedra by spherical triangle

In the figure, peaks can be detected, considering the Wythoff symbol: R|d 2 - n edges of m-gons here R=2 and R-gons degenerate line. Question 2|p - 3 edges, 2P-gons, m-gons, 2P-gons, the vertices of Fig. 2P.question.2P. 2|R - 4 ribs, alternating ...

                                               

List of uniform polyhedra by vertex figure

There are many connections between Uniform polyhedra. Some are obtained by truncating the vertices of a regular polyhedron and quasiregular. Others share the same vertices and edges as other polyhedron. The grouping below exhibit some of these re ...

                                               

List of uniform polyhedra by Wythoff symbol

All the faces are identical, each edge is identical and each vertex is identical. They all have a Wythoff symbol of the form N|M 2.

                                               

Nonconvex great rhombicosidodecahedron

In geometry nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U-67. It has 62 faces, 120 edges, and 60 vertices. It is also called quasirhombicosidodecahedron. It is given a Schlafli symbol T 0.2 { 5 ⁄ 3.3}. His ...

                                               

Truncated dodecadodecahedron

In geometry, the truncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as 59. It is given a Schlafli symbol T 0.1.2 { 5 ⁄ 3.5}. It has 54 faces, 180 edges, and 120 vertices. The Central region of the polyhedron is connected to t ...

                                               

Uniform star polyhedron

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra, implies a self-intersecting. Each polyhedron can contain star polygon faces, star polygon shapes, or both. Compl ...

                                               

Quasiregular polyhedra

                                               

Rhombic enneacontahedron

In the rhombic enneacontahedron is a polyhedron composed of 90 rhombic faces, three, five, or six rhombi meeting at each vertex. It has 60 broad rhombi and 30 slim. In the rhombic enneacontahedron is a zonohedron with a superficial resemblance to ...

                                               

Rhombic hectotriadiohedron

In geometry, the rhombic hectotriadiohedron, rhombhectotriadiohedron or rhombic 132 hedron is a polyhedron composed of 132 rhombic faces. Rhombic facets are 5 positions in the octahedral symmetry. There are two topological types with the same num ...

                                               

5-cell

In geometry, a 5-cell is a four-dimensional object bounded 5 tetrahedral cells. It is also known as p-5, pentachoron, pentatope, pentahedroid, or four-sided pyramid. This is a 4-simplex, the simplest convex regular 4-polytope, and is analogous te ...

                                               

16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope. This is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schlafli in the middle of the 19th century. This is also known as c 16, he ...

                                               

24-cell

In geometry, the 24-cell is the convex regular 4-polytope with Schlafli symbol {3.4.3}. This is also known as 24 C, or icositetrachoron, octaplex, icosatetrahedroid, octacube, Hyper-diamond or polyoctahedron, constructed of octahedral cells. The ...

                                               

600-cell

In geometry, the 600-cell is the convex regular 4-polytope with Schlafli symbol {3.3.5}. Its called 600, hexacosichoron and hexacosihedroid. 600-cell is considered as 4-dimensional analog of the icosahedron, since it has five meeting tetrahedrons ...

                                               

3-3 duoprism

In geometry of 4 dimensions, 3-3 or triangular duoprism is a four-dimensional polyhedron. It can be constructed as the Cartesian product of two triangles and the simplest of an infinite family of four-dimensional polytopes are constructed as the ...

                                               

3-4 duoprism

In geometry in 4 dimensions, 3-4 duoprism, the second smallest p-q duoprism is a 4-polytope in the result of the Cartesian product of a triangle and a Square. 3-4 duoprism exist in some uniform 5-polytopes in the family B5.

                                               

5-5 duoprism

In geometry of 4 dimensions, 5-5 or pentagonal duoprism duoprism-polygonal duoprism, a 4-polytope as the result of the Cartesian product of two pentagons. It has 25 vertices, edges, 50, 35 facade 25 squares, pentagons, and 10 pentagonal prism cel ...

                                               

6-6 duoprism

In geometry of 4 dimensions, 6-6 duoprism or hexagonal-polygonal duoprism, a 4-polytope as the result of the Cartesian product of two hexagons. It has 36 vertices, 72 edges, 48 faces 36 squares and 12 hexagons, 12 hexagonal prism cells. It has Co ...

                                               

6-8 duoprism

3-4 duoantiprism striping 6-8 duoprism, but not evenly. It has the highest symmetry of the construction of approximately 48, 20 cells, consisting of 6 square antiprisms, 8 octahedra as triangular antiprisms, and 24 tetrahedra as digonal disphenoi ...

Encyclopedic dictionary

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