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Stewart Toroid
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a -holed torus), having a topological genus () of 1 or greater. Notable examples include the Császár and Szilassi polyhedra. Variations in definition Toroidal polyhedra are defined as collections of polygons that meet at their edges and vertices, forming a manifold as they do. That is, each edge should be shared by exactly two polygons, and at each vertex the edges and faces that meet at the vertex should be linked together in a single cycle of alternating edges and faces, the link of the vertex. For toroidal polyhedra, this manifold is an orientable surface. Some authors restrict the phrase "toroidal polyhedra" to mean more specifically polyhedra topologically equivalent to the (genus 1) torus. In this area, it is important to distinguish embedded toroidal polyhedra, whose faces are flat polygons in three-dimensional Euclidean space that do not cross themselves or each other, from abstract pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Torus
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A '' regular hexagon'' has Schläfli symbol and can also be constructed as a truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries (''rotational symmetry of order six'') and six reflection symmetries (''six lines of symmetry''), making up the dihedral group D6. The longest diagonals of a regul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple and star polygons. Branko Grünbaum identified two primary definitions used by Johannes Kepler, one being the regular star polygons with intersecting edges that don't generate new vertices, and the second being simple isotoxal concave polygons. The first usage is included in polygrams which includes polygons like the pentagram but also compound figures like the hexagram. One definition of a ''star polygon'', used in turtle graphics, is a polygon having 2 or more turns (turning number and density), like in spirolaterals.Abelson, Harold, diSessa, Andera, 1980, ''Turtle Geometry'', MIT Press, p.24 Etymology Star polygon names combine a numeral prefix, such as ''penta-'', with the Greek suffix '' -gram'' (in this cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eight Octahedra Toroid
8 is a number, numeral, and glyph. 8 or eight may also refer to: Years * AD 8, the eighth year of the AD era * 8 BC, the eighth year before the AD era Art *The Eight (Ashcan School), a group of twentieth century painters associated with the Ashcan School *The Eight (painters), an avant-garde art movement of Hungarian painters Motor vehicles *Bentley Eight, Bentley's "entry-level" offering from 1984 until 1992 *Leyland Eight, a luxury car produced by Leyland Motors from 1920 to 1923 *Mercury Eight, a first Post War Mercury car design *Morris Eight, a small car inspired by the Ford Model Y *Standard Eight, a small car produced by Standard Motor Company 1938–59 *Wolseley Eight, a four-door, light saloon car produced by Wolseley Motors Limited from 1946 to 1948 *Straight eight, automobile engine *Eight cylinder, automobile engine Sports *Eight (rowing), rowing boat used in the sport of competitive rowing *Figure 8 (belay device), rock climbing equipment also known as an "eight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
