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The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. Multiples of it can be stacked to fill a space much like hexagons fill a plane; the cells in a honeycomb have a shape similar to the rhombic dodecahedron cut in half. Download high resolution version (849x754, 59 KB)Rhombic dodecahedron, made by me using POV-Ray, see image:poly. ...
Spinning rhombic dodecahedron, made by me using POV-Ray, see image:poly. ...
A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ...
This shape is a rhombus In geometry, a rhombus (also known as a rhomb) is a quadrilateral in which all of the sides are of equal length. ...
In geometry, a face configuration is notational description of a face-uniform polyhedron. ...
The symmetry group of an object (e. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
Look up Convex set in Wiktionary, the free dictionary. ...
In geometry, a polyhedron is face-uniform when all its faces have the same shape and size (technically, when all faces are congruent). ...
In geometry, a form is edge-uniform if its symmetries act transitively on its edges. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
Look up Convex set in Wiktionary, the free dictionary. ...
This article is about the geometric shape. ...
This shape is a rhombus In geometry, a rhombus (also known as a rhomb) is a quadrilateral in which all of the sides are of equal length. ...
A regular hexagon In geometry, a hexagon is a polygon with six edges and six vertices. ...
Honeycomb on a Langstroth frame A honeycomb is a mass of hexagonal wax cells built by honeybees in their nests to contain their larvae and stores of honey and pollen. ...
It is the polyhedral dual of the cuboctahedron and a zonohedron. The long diagonal of each face is exactly √2 times the length of the short diagonal, so that the acute angles on each face measure 2 tan−1(1/√2), or approximately 70.53°. In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
The square root of two is the positive real number which, when multiplied by itself, gives a product of two. ...
Look up acute in Wiktionary, the free dictionary. ...
Being the dual of an Archimedean polyhedron, the rhombic dodecahedron is face-uniform, meaning the symmetry group of the solid acts transitively on the 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 is also somewhat special in being one of the nine edge-uniform convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron and the rhombic triacontahedron. In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ...
The symmetry group of an object (e. ...
In grammar, a verb is transitive if it takes an object. ...
A sphere rotating around its axis. ...
IT IS KNOWN AS MARK a lunitice insain int gw brain ...
In solid geometry and some ancient physical theories, a Platonic solid is a convex polyhedron with: All its faces being congruent regular polygons The same number of faces meeting at each of its vertices These are in contrast to: The Kepler-Poinsot solids, which are not convex The Archimedean and...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. ...
The Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. ...
The rhombic dodecahedron can be used to tessellate 3-dimensional space. This tessellation can be seen as the Voronoi tessellation of the face-centred cubic lattice. Honeybees use the geometry of rhombic dodecahedra to form honeycomb from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron. Space tesselation of rhombic dodecahedra. ...
Space tesselation of rhombic dodecahedra. ...
The rhombic dodecahedra honeycomb is a tessellation (or honeycomb) in Euclidean 3-space. ...
A tessellated plane seen in street pavement. ...
This is the Voronoi diagram of a random set of points in the plane (all points lie within the image). ...
Rose des Sables (Sand Rose), formed of gypsum crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ...
Species Apis andreniformis Apis cerana, or eastern honey bee Apis dorsata, or giant honey bee Apis florea Apis koschevnikovi Apis laboriosa Apis mellifera, or western honey bee Apis nigrocincta Apis nuluensis Honey bees are a subset of bees which represent a far smaller fraction of bee diversity than most people...
Honeycomb on a Langstroth frame A honeycomb is a mass of hexagonal wax cells built by honeybees in their nests to contain their larvae and stores of honey and pollen. ...
The rhombic dodecahedron forms the hull of the vertex-first projection of a tesseract to 3 dimensions. There are exactly two ways of decomposing a rhombic dodecahedron into 4 congruent parallelepipeds, giving 8 possible parallelepipeds. The 8 cells of the tesseract under this projection map precisely to these 8 parallelepipeds. Stereographic projection In geometry, the tesseract is the 4-dimensional analog of the (3-dimensional) cube, where motion along the fourth dimension is often a representation for bounded transformations of the cube through time. ...
In geometry, a parallelepiped (pronounced ; meaning of parallel planes) or parallelopipedon is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ...
Cartesian coordinates
The eight vertices where three faces meet at their obtuse angles have Cartesian coordinates Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
- (±1, ±1, ±1)
The six vertices where four faces meet at their acute angles are given by the permutations of - (0, 0, ±2)
See also The Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. ...
The truncated rhombic dodecahedron is a convex polyhedron constructed from the rhombic dodecahedron by truncated the 6 (order 4) vertices. ...
External links - Rhombic Dodecahedron – from MathWorld
- Virtual Reality Polyhedra – The Encyclopedia of Polyhedra
- Rhombic Dodecahedron Calendar – make a rhombic dodecahedron calendar without glue
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