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Cuploid
In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles. If the triangles are equilateral and the rectangles are squares, while the base and its opposite face are regular polygons, the triangular, square, and pentagonal cupolae all count among the Johnson solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively. A cupola can be seen as a prism where one of the polygons has been collapsed in half by merging alternate vertices. A cupola can be given an extended Schläfli symbol representing a regular polygon joined by a parallel of its truncation, or Cupolae are a subclass of the prismatoids. Its dual contains a shape that is sort of a weld between half of an -sided trapezohedron and a -sided pyramid. Examples The triangular, square, and pentagonal cupolae are the only non-tri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahemihexahedron
In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges, and 6 vertices. Its vertex figure is a crossed quadrilateral. Its Coxeter–Dynkin diagram is (although this is a double covering of the tetrahemihexahedron). The tetrahemihexahedron is the only non-prismatic uniform polyhedron with an odd number of faces. Its Wythoff symbol is 3/2 3 , 2, but that represents a double covering of the tetrahemihexahedron with eight triangles and six squares, paired and coinciding in space. (It can more intuitively be seen as two coinciding tetrahemihexahedra.) The tetrahemihexahedron is a hemipolyhedron. The "hemi" part of the name means some of the faces form a group with half as many members as some regular polyhedron—here, three square faces form a group with half as many faces as the regular hexahedron, better known as the cube—hence ''hemihexahedron''. Hemi faces are also oriented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertex (geometry), vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edge (geometry), edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e., an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is Cuboctahedron#Radial equilateral symmetry, radially equilateral. Its dual polyhedron is the rhombic dodecahedron. Construction The cuboctahedron can be constructed in many ways: * Its construction can be started by attaching two regular triangular cupolas base-to-base. This is similar to one of the Johnson solids, triangular orthobicupola. The difference is that the triangular orthobicupola is constructed with one of the cupolas twisted so that similar polygonal faces are adjacent, whereas the cuboctahedron is not. As a result, the cuboctahedron may also called the ''triangular gyro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cupola 40
In architecture, a cupola () is a relatively small, usually dome-like structure on top of a building often crowning a larger roof or dome. Cupolas often serve as a roof lantern to admit light and air or as a lookout. The word derives, via Italian, from lower Latin ''cupula'' (classical Latin ''cupella''), (Latin ''cupa''), indicating a vault resembling an upside-down cup. The cylindrical drum underneath a larger cupola is called a tholobate. Background The cupola evolved during the Renaissance from the older oculus. Being weatherproof, the cupola was better suited to the wetter climates of northern Europe. The chhatri, seen in Indian architecture, fits the definition of a cupola when it is used atop a larger structure. Cupolas often serve as a belfry, belvedere, or roof lantern above a main roof. In other cases they may crown a spire, tower, or turret. Barns often have cupolas for ventilation. Cupolas can also appear as small buildings in their own right. The square, dom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex polygon, convex'' or ''star polygon, star''. In the limit (mathematics), limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a Line (geometry), straight line), if the edge length is fixed. General properties These properties apply to all regular polygons, whether convex or star polygon, star: *A regular ''n''-sided polygon has rotational symmetry of order ''n''. *All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. *Together with the property of equal-length sides, this implies that every regular polygon also h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Prism
In geometry, a triangular prism or trigonal prism is a Prism (geometry), prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a ''right triangular prism''. A right triangular prism may be both Semiregular polyhedron, semiregular and Uniform polyhedron, uniform. The triangular prism can be used in constructing another polyhedron. Examples are some of the Johnson solids, the truncated right triangular prism, and Schönhardt polyhedron. Properties A triangular prism has 6 vertices, 9 edges, and 5 faces. Every prism has 2 congruent faces known as its ''bases'', and the bases of a triangular prism are triangles. The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. If the prism's edges are perpendicular to the base, the lateral faces are rectangles, and the prism is called a ''right triangular prism''. This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagon
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 is defined as a hexagon that is both equilateral and equiangular. In other words, a hexagon is said to be regular if the edges are all equal in length, and each of its internal angle is equal to 120°. The Schläfli symbol denotes this polygon as \ . However, the regular hexagon can also be considered as the cutting off the vertices of an equilateral triangle, which can also be denoted as \mathrm\ . A regular hexagon 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). Measurement The longest diagonals of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tile 3464
Tiles are usually thin, square or rectangular coverings manufactured from hard-wearing material such as ceramic, stone, metal, baked clay, or even glass. They are generally fixed in place in an array to cover roofs, floors, walls, edges, or other objects such as tabletops. Alternatively, tile can sometimes refer to similar units made from lightweight materials such as perlite, wood, and mineral wool, typically used for wall and ceiling applications. In another sense, a tile is a construction tile or similar object, such as rectangular counters used in playing games (see tile-based game). The word is derived from the French word ''tuile'', which is, in turn, from the Latin word ''tegula'', meaning a roof tile composed of fired clay. Tiles are often used to form wall and floor coverings, and can range from simple square tiles to complex or mosaics. Tiles are most often made of ceramic, typically glazed for internal uses and unglazed for roofing, but other materials are also com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyramid
A pyramid () is a structure whose visible surfaces are triangular in broad outline and converge toward the top, making the appearance roughly a pyramid in the geometric sense. The base of a pyramid can be of any polygon shape, such as triangular or quadrilateral, and its surface-lines either filled or stepped. A pyramid has the majority of its mass closer to the ground with less mass towards the pyramidion at the apex. This is due to the gradual decrease in the cross-sectional area along the vertical axis with increasing elevation. This offers a weight distribution that allowed early civilizations to create monumental structures.Ancient civilizations in many parts of the world pioneered the building of pyramids. The largest pyramid by volume is the Mesoamerican Great Pyramid of Cholula, in the Mexican state of Puebla. For millennia, the largest structures on Earth were pyramids—first the Red Pyramid in the Dashur Necropolis and then the Great Pyramid of Khufu, bot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapezohedron
In geometry, an trapezohedron, -trapezohedron, -antidipyramid, -antibipyramid, or -deltohedron Remarks: the faces of a deltohedron are deltoids; a (non-twisted) kite or deltoid can be Dissection (geometry), dissected into two isosceles triangles or "deltas" (Δ), base-to-base. is the dual polyhedron of an antiprism. The faces of an are Congruence (geometry), congruent and symmetrically staggered; they are called #Symmetry, ''twisted kites''. With a higher symmetry, its faces are Kite (geometry), ''kites'' (sometimes also called ''trapezoids'', or ''deltoids''). The "" part of the name does not refer to faces here, but to two arrangements of each Vertex (geometry), vertices around an axis of symmetry. The dual antiprism has two actual faces. An trapezohedron can be Dissection (geometry), dissected into two equal Pyramid (geometry), pyramids and an antiprism. Terminology These figures, sometimes called deltohedra, are not to be confused with Deltahedron, deltahedra, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet (geometry), facet in place of each vertex. The term originates from Kepler's names for the Archimedean solids. Uniform truncation In general any polyhedron (or polytope) can also be truncated with a degree of freedom as to how deep the cut is, as shown in Conway polyhedron notation truncation operation. A special kind of truncation, usually implied, is a uniform truncation, a truncation operator applied to a regular polyhedron (or regular polytope) which creates a resulting uniform polyhedron (uniform polytope) with equal edge lengths. There are no degrees of freedom, and it represents a fixed geometric, just like the regular polyhedra. In general all single ringed uniform polytopes have a uniform truncation. For example, the icosidodecahedron, represented as Schläfli symbols r or \begin 5 \\ 3 \end, and Coxeter-Dynkin diagram or has a uniform truncation, the truncate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex polygon, convex'' or ''star polygon, star''. In the limit (mathematics), limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a Line (geometry), straight line), if the edge length is fixed. General properties These properties apply to all regular polygons, whether convex or star polygon, star: *A regular ''n''-sided polygon has rotational symmetry of order ''n''. *All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. *Together with the property of equal-length sides, this implies that every regular polygon also h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schläfli Symbol
In geometry, the Schläfli symbol is a notation of the form \ that defines List of regular polytopes and compounds, regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean space, Euclidean geometry to more than three dimensions and discovered all their convex regular polytopes, including the six that occur in four dimensions. Definition The Schläfli symbol is a Recursive definition, recursive description, starting with \ for a p-sided regular polygon that is Convex set, convex. For example, is an equilateral triangle, is a Square (geometry), square, a convex regular pentagon, etc. Regular star polygons are not convex, and their Schläfli symbols \ contain irreducible fractions p/q, where p is the number of vertices, and q is their turning number. Equivalently, \ is created from the vertices of \, connected every q. For example, \ is a pentagram; \ is a pentagon. A regular pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
