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Decagram (geometry)
In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is . The name ''decagram'' combines a numeral prefix, ''wikt:deca-, deca-'', with the Greek language, Greek suffix ''wikt:-gram, -gram''. The ''-gram'' suffix derives from ''γραμμῆς'' (''grammēs'') meaning a line. Regular decagram For a regular decagram with unit edge lengths, the proportions of the crossing points on each edge are as shown below. Applications Decagrams have been used as one of the decorative motifs in girih tiles. : Isotoxal variations An isotoxal polygon has two vertices and one edge. There are isotoxal decagram forms, which alternates vertices at two radii. Each form has a freedom of one angle. The first is a variation of a double-wound of a pentagon , and last is a variation of a double-wound of a pentagram . The middle is a variation of a regular decagram, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sultan Barquq's Qur'an Decagram
Sultan (; ', ) is a Royal and noble ranks, position with several historical meanings. Originally, it was an Arabic abstract noun meaning "strength", "authority", "rulership", derived from the verbal noun ', meaning "authority" or "power". Later, it came to be used as the title of certain rulers who claimed almost full sovereignty (i.e., not having dependence on any higher ruler) without claiming the overall caliphate, or to refer to a powerful governor of a province within the caliphate. The adjectival form of the word is "sultanic", and the State (polity), state and territories ruled by a sultan, as well as his office, are referred to as a sultanate ( '). The term is distinct from king ( '), though both refer to a sovereign ruler. The use of "sultan" is restricted to Muslim countries, where the title carries religious significance, contrasting the more secular ''king'', which is used in both Muslim and non-Muslim countries. Brunei, Malaysia and Oman are the only sovereign s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decagon
In geometry, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided polygon or 10-gon.. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon A '' regular decagon'' has all sides of equal length and each internal angle will always be equal to 144°. Its Schläfli symbol is and can also be constructed as a truncated pentagon, t, a quasiregular decagon alternating two types of edges. Side length The picture shows a regular decagon with side length a and radius R of the circumscribed circle. * The triangle E_E_1M has two equally long legs with length R and a base with length a * The circle around E_1 with radius a intersects ]M\,E_ in a point P (not designated in the picture). * Now the triangle \; is an isosceles triangle">/math> in a point P (not designated in the picture). * Now the triangle \; is an isosceles triangle with vertex E_1 and with base angles m\angle E_1 E_ P = m\angle E_ P E_1 = 72 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Great Icosahedron And Great Stellated Dodecahedron
There are two different compounds of great icosahedron and great stellated dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron, the other is a stellation of the icosidodecahedron. Dual compound It can be seen as a polyhedron compound of a great icosahedron and great stellated dodecahedron. It is one of five compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It is a stellation of the great icosidodecahedron. It has icosahedral symmetry (I''h'') and it has the same vertex arrangement as a great rhombic triacontahedron. This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ( " decagram"); this series continues into the fourth dimension as compounds of star 4-polytopes. Stellation of the icosidodecahedron This polyhedron is a stellation of the icosidodecahedron In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Small Stellated Dodecahedron And Great Dodecahedron
In geometry, the great dodecahedron is one of four Kepler–Poinsot polyhedra. It is composed of 12 pentagonal faces (six pairs of parallel pentagons), intersecting each other making a pentagrammic path, with five pentagons meeting at each vertex. Construction One way to construct a great dodecahedron is by faceting the regular icosahedron. In other words, it is constructed from the regular icosahedron by removing its polygonal faces without changing or creating new vertices. For each vertex of the icosahedron, the five neighboring vertices become those of a regular pentagon face of the great dodecahedron. The resulting shape has a pentagram as its vertex figure, so its Schläfli symbol is \ . The great dodecahedron may also be interpreted as the ''second stellation of dodecahedron''. The construction started from a regular dodecahedron by attaching 12 pentagonal pyramids onto each of its faces, known as the ''first stellation''. The second stellation appears when 30 wedges ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Polytope
In geometry, a pentagonal polytope is a regular polytope in ''n'' dimensions constructed from the H''n'' Coxeter group. The family was named by H. S. M. Coxeter, because the two-dimensional pentagonal polytope is a pentagon. It can be named by its Schläfli symbol as (dodecahedral) or (icosahedral). Family members The family starts as 1-polytopes and ends with ''n'' = 5 as infinite tessellations of 4-dimensional hyperbolic space. There are two types of pentagonal polytopes; they may be termed the ''dodecahedral'' and ''icosahedral'' types, by their three-dimensional members. The two types are duals of each other. Dodecahedral The complete family of dodecahedral pentagonal polytopes are: # Line segment, # Pentagon, # Dodecahedron, (12 pentagonal faces) # 120-cell, (120 dodecahedral cells) # Order-3 120-cell honeycomb, (tessellates hyperbolic 4-space (∞ 120-cell facets) The facets of each dodecahedral pentagonal polytope are the dodecahedral pentagonal polytopes of on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of 120-cell And 600-cell
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called a C120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron and hecatonicosahedroid. The boundary of the 120-cell is composed of 120 dodecahedral cells with 4 meeting at each vertex. Together they form 720 pentagonal faces, 1200 edges, and 600 vertices. It is the 4- dimensional analogue of the regular dodecahedron, since just as a dodecahedron has 12 pentagonal facets, with 3 around each vertex, the ''dodecaplex'' has 120 dodecahedral facets, with 3 around each edge. Its dual polytope is the 600-cell. Geometry The 120-cell incorporates the geometries of every convex regular polytope in the first four dimensions (except the polygons and above). As the sixth and largest regular convex 4-polytope, it contains inscribed instances of its four predecessors (recursi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Dodecahedron And Icosahedron
In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound. As a compound It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It has icosahedral symmetry (I''h'') and the same vertex arrangement as a rhombic triacontahedron. This can be seen as the three-dimensional equivalent of the compound of two pentagons ( " decagram"); this series continues into the fourth dimension as the compound of 120-cell and 600-cell and into higher dimensions as compounds of hyperbolic tilings. As a stellation This polyhedron is the first stellation of the icosidodecahedron, and given as Wenninger model index 47. The stellation facets for construction are: : As a Faceting The compound of a Dodecahedron and an Icosahedron shares the same vertices as a list of other polyhedra, including the Rhombic triacontahedron and the Small tria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Star Figure 5(2,1)
Regular may refer to: Arts, entertainment, and media Music * "Regular" (Badfinger song) * Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings Other uses * Regular character, a main character who appears more frequently and/or prominently than a recurring character * Regular division of the plane, a series of drawings by the Dutch artist M. C. Escher which began in 1936 Language * Regular inflection, the formation of derived forms such as plurals in ways that are typical for the language ** Regular verb * Regular script, the newest of the Chinese script styles Mathematics Algebra and number theory * Regular category, a kind of category that has similarities to both Abelian categories and to the category of sets * Regular chains in computer algebra * Regular element (other), certain kinds of elements of an algebraic structure * Regular extension of fields * Regular ideal (multiple definitions) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
