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Rhombic Polyhedron
Rhombic may refer to: *Rhombus, a quadrilateral whose four sides all have the same length (often called a diamond) *Rhombic antenna, a broadband directional antenna most commonly used on shortwave frequencies * polyhedra formed from rhombuses, such as the rhombic dodecahedron or the rhombic triacontahedron or the rhombic dodecahedral honeycomb or the rhombic icosahedron or the rhombic hexecontahedron or the rhombic enneacontahedron or the trapezo-rhombic dodecahedron * other things that exhibit the shape of a rhombus, such as rhombic tiling, Rhombic Chess, rhombic drive, Rhombic Skaapsteker, rhombic egg eater, rhombic night adder, forest rhombic night adder {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombus
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (which some authors call a calisson after the French sweet – also see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle. Every rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. A rhombus with right angles is a square. Etymology The word "rhombus" comes from grc, ῥόμβος, rhombos, meaning something that spins, which derives from the verb , romanized: , meaning "to turn round and round." The word was used both by Eucl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Antenna
A rhombic antenna is made of four sections of wire suspended parallel to the ground in a diamond or "rhombus" shape. Each of the four sides is the same length – about a quarter-wavelength to one wavelength per section – converging but not touching at an angle of about 42° at the fed end and at the far end. The length is not critical, typically from one to two wavelengths ( λ), but there is an optimum angle for any given length and frequency. A horizontal rhombic antenna radiates horizontally polarized radio waves at a low elevation angle off the pointy ends of the antenna. If the sections are joined by a resistor at either of the acute (pointy) ends, then the antenna will receive from and transmit to only the direction the end with the resistor points at. Its principal advantages over other types of antenna are its simplicity, high forward gain, wide bandwidth, and the ability to operate over a wide range of frequencies. Description A rhombic antenna consists of one to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron. Properties The rhombic dodecahedron is a zonohedron. Its polyhedral dual is the cuboctahedron. The long face-diagonal length is exactly times the short face-diagonal length; thus, the acute angles on each face measure arccos(), or approximately 70.53°. Being the dual of an Archimedean polyhedron, the rhombic dodecahedron is face-transitive, meaning the symmetry group of the solid acts transitively on its set of faces. In elementary terms, this means that for any two faces A and B, there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B. The rhombic dodecahedron can be viewed as the convex hull of the union of the vertices of a cube and an octahedron. The 6 vertices where 4 rhombi meet correspond t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Triacontahedron
In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron. The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, , so that the acute angles on each face measure or approximately 63.43°. A rhombus so obtained is called a ''golden rhombus''. Being the dual of an Archimedean solid, the rhombic triacontahedron is ''face-transitive'', meaning the symmetry group of the solid acts transitively on the set of faces. This means that for any two faces, and , there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face to face . The rhombic triacontahedron is somewhat special in being one of the nine edge-transitive c ... [...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] |
Rhombic Icosahedron
The rhombic icosahedron is a polyhedron shaped like an oblate sphere. Its 20 faces are congruent golden rhombi; 3, 4, or 5 faces meet at each vertex. It has 5 faces (green on top figure) meeting at each of its 2 poles; these 2 vertices lie on its axis of 5-fold symmetry, which is perpendicular to 5 axes of 2-fold symmetry through the midpoints of opposite equatorial edges (example on top figure: most left-hand and most right-hand mid-edges). Its other 10 faces follow its equator, 5 above and 5 below it; each of these 10 rhombi has 2 of its 4 sides lying on this zig-zag skew decagon equator. The rhombic icosahedron has 22 vertices. It has D5d, +,10 (2*5) symmetry group, of order 20; thus it has a center of symmetry (since 5 is odd). Even though all its faces are congruent, the rhombic icosahedron is not face-transitive, since one can distinguish whether a particular face is near the equator or near a pole by examining the types of vertices surrounding this face. Zonohedron T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Hexecontahedron
In geometry, a rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry. It was described mathematically in 1940 by Helmut Unkelbach. It is topologically identical to the convex deltoidal hexecontahedron which has kite faces. Dissection The rhombic hexecontahedron can be dissected into 20 acute golden rhombohedra meeting at a central point. This gives the volume of a hexecontahedron of side length ''a'' to be V = (10 + 2\sqrt 5)a^3 and the area to be A = (24\sqrt 5)a^2. : Construction A rhombic hexecontahedron can be constructed from a regular dodecahedron, by taking its vertices, its face centers and its edge centers and scaling them in or out from the body center to different extents. Thus, if the 20 vertices of a dodecahedron are pulled out to increase the circumradius by a factor of ( ϕ+1)/2 ≈ 1.309, the 12 face centers are pushed in to decrease the inradius to (3-ϕ)/2 ≈ 0.691 of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Enneacontahedron
In geometry, a rhombic enneacontahedron (plural: rhombic enneacontahedra) is a polyhedron composed of 90 Rhombus, rhombic faces; with three, five, or six rhombi meeting at each vertex. It has 60 broad rhombi and 30 slim. The rhombic enneacontahedron is a zonohedron with a superficial resemblance to the rhombic triacontahedron. Construction It can also be seen as a nonuniform truncated icosahedron with pyramids augmented to the pentagonal and hexagonal faces with heights adjusted until the dihedral angles are zero, and the two pyramid type side edges are equal length. This construction is expressed in the Conway polyhedron notation ''jtI'' with join operator ''j''. Without the equal edge constraint, the wide rhombi are kite (geometry), kites if limited only by the icosahedral symmetry. The sixty broad rhombic faces in the rhombic enneacontahedron are identical to those in the rhombic dodecahedron, with diagonals in a ratio of 1 to the square root of 2. The face angles of these rho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapezo-rhombic Dodecahedron
In geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex dodecahedron with 6 rhombic and 6 trapezoidal faces. It has symmetry. A concave form can be constructed with an identical net, seen as excavating trigonal trapezohedra from the top and bottom. Construction This polyhedron could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom. The trapezoids represent what remains of the original prism sides, and the 6 rhombi a result of the top and bottom cuts. Space-filling tessellation A space-filling tessellation, the trapezo-rhombic dodecahedral honeycomb, can be made by translated copies of this cell. Each "layer" is a hexagonal tiling, or a rhombille tiling, and alternate layers are connected by shifting their centers and rotating each polyhedron so the rhombic faces match up. :: In the special case that the long sides of the trapezoids equals twice the length of the short sides, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Tiling
In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombus, rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called Polyiamond, diamonds. Sets of three rhombi meet at their 120° angles, and sets of six rhombi meet at their 60° angles. Properties The rhombille tiling can be seen as a subdivision of a hexagonal tiling with each hexagon divided into three rhombi meeting at the center point of the hexagon. This subdivision represents a regular compound tiling. It can also be seen as a subdivision of four hexagonal tilings with each hexagon divided into 12 rhombi. The diagonals of each rhomb are in the ratio 1:. This is the Dual polyhedron, dual tiling of the trihexagonal tiling or kagome lattice. As the dual to a uniform tiling, it is one of eleven possible Laves tilings, and in the face configuration for monohedral til ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Chess
Rhombic chess is a chess variant for two players created by Tony Paletta in 1980.Pritchard (1994), p. 255 The gameboard has an overall hexagonal shape and comprises 72 rhombi in three alternating colors. Each player commands a full set of standard chess pieces. The game was first published in ''Chess Spectrum Newsletter'' 2 by the inventor. It was included in ''World Game Review'' No. 10 edited by Michael Keller. Game rules The diagram shows the starting setup. As in standard chess, White moves first and checkmate wins the game. Piece moves are described using two basic types of movement: * Edgewise—through the common side of adjoining cells. If an edgewise move is more than one step, it continues in a straight line from the side of a cell through its opposite side, the line being orthogonal to these sides. * Pointwise—through the sharpest corner of a cell, in a straight line to the next cell. (The paths are highlighted on the board by same-colored cells.) Piece moves * A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Drive
The rhombic drive is a specific method of transferring mechanical energy, or work, used when a single cylinder is used for two separately oscillating pistons. History It was originally developed around 1900 for the twin-cylinder Lanchester car engine where it allowed perfect balancing of the inertial forces on both pistons. A current example of its use is on beta type-Stirling engines; the drive's complexity and tight tolerances, causing a high cost of manufacture, is a hurdle for the widespread usage of this drive. Operation In its simplest form, the drive utilizes a jointed rhomboid to convert linear work from a reciprocating piston to rotational work. The connecting rod of the piston is rigid as opposed to a common reciprocating engine which directly connects the piston to the crankshaft with a flexible joint in the piston. Instead, the rod connects to one corner of a rhombus. When force is applied to the piston, it pushes down; at the same time, the outer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
