|
Elongated Square Bipyramid
In geometry, the elongated square bipyramid (or elongated octahedron) is one of the Johnson solids (). As the name suggests, it can be constructed by elongating an octahedron by inserting a cube between its congruent halves. It has been named the pencil cube or 12-faced pencil cube due to its shape.Order in Space: A design source book, Keith Critchlow, p.46-47 A zircon crystal is an example of an elongated square bipyramid. Formulae The following formulae for volume (V), surface area (A) and height (H) can be used if all faces are regular, with edge length L: :V = L^3\cdot \left( 1 + \frac\right) \approx L^3\cdot 1.471404521 :A = L^2\cdot \left(4 + 2\sqrt\right) \approx L^2\cdot 7.464101615 :H = L\cdot \left( 1 + \sqrt\right) \approx L\cdot 2.414213562 Dual polyhedron The dual of the elongated square bipyramid is called a square bifrustum and has 10 faces: 8 trapezoidal and 2 square. Related polyhedra and honeycombs A special kind of elongated square bipyrami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides ( ); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform (i.e., not Platonic solid, Archimedean solid, uniform prism, or uniform antiprism) before they refer to it as a “Johnson solid”. As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex. The pentagonal pyramid () is an example that has a degree-5 vertex. Although there is no obvious restriction that any given regular polygon cannot be a face of a Johnson solid, it turns out that the faces of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is about 10,000 m". For example, "Christopher Columbus is 5 foot 2 inches in vertical height." When the term is used to describe vertical position (of, e.g., an airplane) from sea level, height is more often called '' altitude''. Furthermore, if the point is attached to the Earth (e.g., a mountain peak), then altitude (height above sea level) is called ''elevation''. In a two-dimensional Cartesian space, height is measured along the vertical axis (''y'') between a specific point and another that does not have the same ''y''-value. If both points happen to have the same ''y''-value, then their relative height is zero. In the case of three-dimensional space, height is measured along the vertical ''z'' axis, describing a distance from (or "above ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chamfered Square Tiling
In geometry, the chamfered square tiling or semitruncated square tiling is a tiling of the Euclidean plane. It is a square tiling with each edge chamfered into new hexagonal faces. It can also be seen as the intersection of two truncated square tilings with offset positions. And its appearance is similar to a truncated square tiling, except only half of the vertices have been truncated, leading to its descriptive name ''semitruncated square tiling''. Usage and Names in tiling patterns In floor tiling, this pattern with small squares has been labeled as ''Metro Broadway Matte'' and ''alternate corner square tile''. With large squares it has been called a ''Dijon tile pattern''. As 3 rows of rectangles, it has been called a ''basketweave tiling'' and ''triple block tile pattern ''. Variations Variations can be seen in different degrees of ''truncation''. As well, geometric variations exist within a given symmetry. The second row shows the tilings with a 45 degree rotation whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Pyramid
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has symmetry. If all edge lengths are equal, it is an equilateral square pyramid, the Johnson solid General square pyramid A possibly oblique square pyramid with base length ''l'' and perpendicular height ''h'' has volume: :V=\frac l^2 h. Right square pyramid In a right square pyramid, all the lateral edges have the same length, and the sides other than the base are congruent isosceles triangles. A right square pyramid with base length ''l'' and height ''h'' has surface area and volume: :A=l^2+l\sqrt, :V=\frac l^2 h. The lateral edge length is: :\sqrt; the slant height is: :\sqrt. The dihedral angles are: :*between the base and a side: :::\arctan \left(\right); :*between two sides: :::\arccos \left(\right). Equilateral square pyramid, Johnson solid J1 If all edges have the same length, then the sides ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Dodecahedral Honeycomb
The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see Kepler conjecture). Geometry It consists of copies of a single cell, the rhombic dodecahedron. All faces are rhombi, with diagonals in the ratio 1:. Three cells meet at each edge. The honeycomb is thus cell-transitive, face-transitive, and edge-transitive; but it is not vertex-transitive, as it has two kinds of vertex. The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing. Colorings Cells can be given 4 colors in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Honeycomb
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol . John Horton Conway called this honeycomb a cubille. Related honeycombs It is part of a multidimensional family of hypercube honeycombs, with Schläfli symbols of the form , starting with the square tiling, in the plane. It is one of 28 uniform honeycombs using convex uniform polyhedral cells. Isometries of simple cubic lattices Simple cubic lattices can be distorted into lower symmetries, represented by lower crystal systems: Uniform colorings There is a large number of uniform colorings, derived from different symmetries. These include: Projections The ''cubic honeycomb'' can be orthogonally projected into the euclidean plane with various symmetry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elongated Oblate Octahedron Net
Elongation may refer to: * Elongation (astronomy) * Elongation (geometry) * Elongation (plasma physics) * Part of transcription of DNA into RNA of all types, including mRNA, tRNA, rRNA, etc. * Part of translation (biology) of mRNA into proteins * Elongated organisms * Stretch ratio In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can ... in the physics of deformation See also * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elongated Oblate Octahedron
Elongation may refer to: * Elongation (astronomy) * Elongation (geometry) * Elongation (plasma physics) * Part of transcription of DNA into RNA of all types, including mRNA, tRNA, rRNA, etc. * Part of translation (biology) of mRNA into proteins * Elongated organisms * Stretch ratio In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can ... in the physics of deformation See also * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Elongated Square Dipyramid Net
Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical number), a grammatical category used in some languages * Dual county, a Gaelic games county which in both Gaelic football and hurling * Dual diagnosis, a psychiatric diagnosis of co-occurrence of substance abuse and a mental problem * Dual fertilization, simultaneous application of a P-type and N-type fertilizer * Dual impedance, electrical circuits that are the dual of each other * Dual SIM cellphone supporting use of two SIMs * Aerochute International Dual a two-seat Australian powered parachute design Acronyms and other uses * Dual (brand), a manufacturer of Hifi equipment * DUAL (cognitive architecture), an artificial intelligence design model * DUAL algorithm, or diffusing update algorithm, used to update Internet protocol routi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Elongated Square Dipyramid
Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical number), a grammatical category used in some languages * Dual county, a Gaelic games county which in both Gaelic football and hurling * Dual diagnosis, a psychiatric diagnosis of co-occurrence of substance abuse and a mental problem * Dual fertilization, simultaneous application of a P-type and N-type fertilizer * Dual impedance, electrical circuits that are the dual of each other * Dual SIM cellphone supporting use of two SIMs * Aerochute International Dual a two-seat Australian powered parachute design Acronyms and other uses * Dual (brand), a manufacturer of Hifi equipment * DUAL (cognitive architecture), an artificial intelligence design model * DUAL algorithm, or diffusing update algorithm, used to update Internet protocol routi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
