dodecahedra वाक्य
उदाहरण वाक्य
मोबाइल
- Honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron.
- About a hundred of these dodecahedra have been found from Wales to Hungary and Spain and to the east of Italy, with most found in Germany and France.
- In 20th-century art, dodecahedra appear in the work of M . C . Escher, such as his lithographs " Gravitation " ( 1952 ).
- The unfolded cube can be stellated rhombic dodecahedra, each of which comprise half the volume of the original cube, making it a kind of three-dimensional dissection puzzle.
- There is another honeycomb in hyperbolic 3-space called the order-4 dodecahedral honeycomb, { 5, 3, 4 }, which has only four dodecahedra per edge.
- It can be constructed by creating two coinciding dodecahedra in 3-space, and translating each copy in opposite perpendicular directions in 4-space until their separation equals their edge length.
- This family has order 120 & times; 120 = 24 & times; 600 = 14400 : 120 for each of the 120 dodecahedra, or 24 for each of the 600 tetrahedra.
- These projections are also used in showing the four-dimensional 120-cell, a regular 4-dimensional polytope, constructed from 120 dodecahedra, projecting it down to 3-dimensions.
- The icosahedron, as a uniform " snub tetrahedron " 25px, is similar to these snub-pair compounds : compound of two snub cubes and compound of two snub dodecahedra.
- Although regular dodecahedra do not exist in crystals, the pyritohedron form occurs in the crystals of the mineral pyrite, and it may be an inspiration for the discovery of the regular Platonic solid form.
- Just as a dodecahedron can be built up as a model with 12 pentagons, 3 around each vertex, the " dodecaplex " can be built up from 120 dodecahedra, with 3 around each edge.
- Examples include " Circoporus octahedrus ", " Circogonia icosahedra ", " Lithocubus geometricus " and " Circorrhegma dodecahedra "; the shapes of these creatures are indicated by their names.
- The great icosahedron, as a uniform " retrosnub tetrahedron " 50px, is similar to these snub-pair compounds : compound of two icosahedra, compound of two snub cubes and compound of two snub dodecahedra.
- The regular hyperbolic honeycombs thus include two with four or five dodecahedra meeting at each edge; their dihedral angles thus are ? / 2 and 2? / 5, both of which are less than that of a Euclidean dodecahedron.
- The small and great stellated dodecahedra, sometimes called the "'Kepler polyhedra "', were first recognized as regular by Johannes Kepler in 1619 . He obtained them by convex, as the traditional Platonic solids were.
- One related non-wythoffian form is constructed from the { 3, 5, 3 } vertex figure with 4 ( tetrahedrally arranged ) vertices removed, creating pentagonal antiprisms and dodecahedra filling in the gaps, called a tetrahedrally diminished dodecahedron.
- These honeycombs are also related to the 120-cell which can be considered as a honeycomb in positively curved space ( the surface of a 4-dimensional sphere ), with three dodecahedra on each edge, { 5, 3, 3 }.
- The vertices in rhombic dodecahedral packing appear to be the centres of tetrahedron or octahedron ( taking the centres of surrounding ) rhombic dodecahedra as vertices-is there a name for this type of ( octahedron / tetrahedron ) / ( rhombic dodecahedron ) dual relationship
- The substance can be seen with empirical formula B 12 C 3 ( i . e ., with B 12 dodecahedra being a motif ), but with less carbon, as the suggested C 3 units are replaced with C-B-C chains, and some smaller ( B 6 ) octahedra are present as well ( see the boron carbide article for structural analysis ).
- There are 6, 384, 634 topologically distinct " convex " dodecahedra, excluding mirror images, having at least 8 vertices . ( Two polyhedra are " topologically distinct " if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces .)
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