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searching for Regular dodecahedron 39 found (104 total)

Great stellated dodecahedron (473 words) [view diff] exact match in snippet view article find links to article

although not its vertex figure or vertex configuration, with the regular dodecahedron, as well as being a stellation of a (smaller) dodecahedron. It is

Compound of ten tetrahedra (364 words) [view diff] exact match in snippet view article find links to article

described by Edmund Hess in 1876. It can be seen as a faceting of a regular dodecahedron. It can also be seen as the compound of ten tetrahedra with full

Dodecahedrane (1,906 words) [view diff] exact match in snippet view article find links to article

whose carbon atoms are arranged as the vertices (corners) of a regular dodecahedron. Each carbon is bound to three neighbouring carbon atoms and to a

Face diagonal (245 words) [view diff] exact match in snippet view article find links to article

cube with side length a is a 2 {\displaystyle a{\sqrt {2}}} . A regular dodecahedron has 60 face diagonals (and 100 space diagonals). Gullberg, Jan (1997)

Seifert–Weber space (462 words) [view diff] exact match in snippet view article find links to article

pentagons is 72°. This does not match the 117° dihedral angle of a regular dodecahedron in Euclidean space, but in hyperbolic space there exist regular dodecahedra

Compound of five cubes (415 words) [view diff] exact match in snippet view article find links to article

first described by Edmund Hess in 1876. Its vertices are those of a regular dodecahedron. Its edges form pentagrams, which are the stellations of the pentagonal

Ditrigonal dodecadodecahedron (210 words) [view diff] exact match in snippet view article find links to article

Wythoff symbol 3 | 5⁄3 5, and Coxeter diagram . Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal

Small ditrigonal icosidodecahedron (154 words) [view diff] exact match in snippet view article find links to article

alternates equilateral triangle and pentagram faces. Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the great ditrigonal

Small stellated dodecahedron (768 words) [view diff] exact match in snippet view article find links to article

but it is included for completeness. Visually, it looks like a regular dodecahedron on the surface, but it has 24 faces in overlapping pairs. The spikes

Hexadecahedron (175 words) [view diff] exact match in snippet view article find links to article

and can be seen topologically by removing 4 of 20 vertices of a regular dodecahedron and is called a tetrahedrally diminished dodecahedron. The following

Great ditrigonal icosidodecahedron (165 words) [view diff] exact match in snippet view article find links to article

its edge, a value it shares with the cube. Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal

Faceting (442 words) [view diff] exact match in snippet view article find links to article

dodecahedron, and great icosahedron. They all have 30 edges. The regular dodecahedron can be faceted into one regular Kepler–Poinsot polyhedron, three

Polyhedral group (420 words) [view diff] exact match in snippet view article find links to article

icosahedral group of order 60, rotational symmetry group of the regular dodecahedron and the regular icosahedron. It is isomorphic to A5. The conjugacy

Rule of twelfths (1,002 words) [view diff] exact match in snippet view article find links to article

A regular dodecahedron (grey) approximated with a lattice polygon using the rule of twelfths (red)

Hippasus (1,513 words) [view diff] exact match in snippet view article find links to article

Pythagorean who drowned at sea for making known the construction of the regular dodecahedron in the sphere. In another account he tells how it was Hippasus who

Polyhedron model (560 words) [view diff] exact match in snippet view article find links to article

A net for the regular dodecahedron

Stellation diagram (348 words) [view diff] exact match in snippet view article find links to article

The stellation diagram for the regular dodecahedron with the central pentagon highlighted. This diagram represents the dodecahedron face itself.

Angular defect (834 words) [view diff] exact match in snippet view article find links to article

falls short of a full circle. The defect of any of the vertices of a regular dodecahedron (in which three regular pentagons meet at each vertex) is 36°, or

Dessin d'enfant (4,171 words) [view diff] exact match in snippet view article find links to article

shows the set of triangles generated in this way starting from a regular dodecahedron. When the regular map lies in a surface whose genus is greater than

90 (number) (2,028 words) [view diff] exact match in snippet view article

Whereas the rhombic enneacontahedron is the zonohedrification of the regular dodecahedron, a honeycomb of Witting polytopes holds vertices isomorphic to the

Schläfli symbol (1,985 words) [view diff] exact match in snippet view article find links to article

faces (the vertex figure is a q-gon). For example, {5,3} is the regular dodecahedron. It has pentagonal (5 edges) faces, and 3 pentagons around each vertex

Stellation (2,189 words) [view diff] exact match in snippet view article find links to article

they meet to form a new polygon or polyhedron. He stellated the regular dodecahedron to obtain two regular star polyhedra, the small stellated dodecahedron

Final stellation of the icosahedron (1,085 words) [view diff] exact match in snippet view article find links to article

spheres. The innermost group of 20 vertices form the vertices of a regular dodecahedron; the next layer of 12 form the vertices of a regular icosahedron;

Paul Schatz (636 words) [view diff] exact match in snippet view article find links to article

sequentially in a circle on the plane—onto the twelve faces of a regular dodecahedron (a solid whose twelve faces are identical pentagons). To preserve

Cairo pentagonal tiling (2,509 words) [view diff] exact match in snippet view article find links to article

each cube vertex, to form the same combinatorial structure as a regular dodecahedron. The other family of pentagons forming the Cairo tiling are pentagons

Kepler conjecture (2,710 words) [view diff] exact match in snippet view article find links to article

sphere in a packing of equal spheres is at least the volume of a regular dodecahedron with inradius 1. McLaughlin's proof, for which he received the 1999

Pyrite (4,467 words) [view diff] exact match in snippet view article find links to article

T-shaped crystals. Pyrite can also form shapes almost the same as a regular dodecahedron, known as pyritohedra, and this suggests an explanation for the artificial

Hyperbolic 3-manifold (2,217 words) [view diff] exact match in snippet view article find links to article

Seifert–Weber space which is obtained by gluing opposite faces of a regular dodecahedron. A variation on this construction is by using hyperbolic Coxeter

Euclid (4,421 words) [view diff] exact match in snippet view article find links to article

Euclid's construction of a regular dodecahedron

Planar graph (4,541 words) [view diff] exact match in snippet view article find links to article

A Schlegel diagram of a regular dodecahedron, forming a planar graph from a convex polyhedron.

Coxeter group (3,763 words) [view diff] exact match in snippet view article find links to article

I2(p), for p ≥ 3. In three dimensions, the symmetry group of the regular dodecahedron and its dual, the regular icosahedron, is H3, known as the full icosahedral

Quasiregular polyhedron (1,523 words) [view diff] exact match in snippet view article find links to article

polyhedra: Lastly there are three ditrigonal forms, all facetings of the regular dodecahedron, whose vertex figures contain three alternations of the two face

Clathrate hydrate (3,692 words) [view diff] exact match in snippet view article find links to article

has the shape of a pentagonal dodecahedron (512) (which is not a regular dodecahedron) and the large one that of a tetradecahedron, specifically a hexagonal

Midsphere (2,932 words) [view diff] exact match in snippet view article find links to article

and φ 2 2 ℓ {\displaystyle {\frac {\varphi ^{2}}{2}}\ell } for a regular dodecahedron. The uniform polyhedra, including the regular, quasiregular and semiregular

Prince Rupert's cube (2,486 words) [view diff] exact match in snippet view article find links to article

Platonic solids—the cube, regular tetrahedron, regular octahedron, regular dodecahedron, and regular icosahedron—have the Rupert property. Of the 13 Archimedean

List of moments of inertia (567 words) [view diff] exact match in snippet view article find links to article

\mathrm {solid} }=I_{z,\mathrm {solid} }={\frac {1}{10}}ms^{2}\,\!} Regular dodecahedron of side s and mass m I x , h o l l o w = I y , h o l l o w = I z

Pythagoreanism (9,382 words) [view diff] exact match in snippet view article find links to article

solids: the tetrahedron, the cube and the dodecahedron. The sides of a regular dodecahedron are regular pentagons, which for Pythagoreans symbolised health.

3-manifold (5,821 words) [view diff] exact match in snippet view article find links to article

pentagons is 72°. This does not match the 117° dihedral angle of a regular dodecahedron in Euclidean space, but in hyperbolic space there exist regular dodecahedra

1000 (number) (24,116 words) [view diff] exact match in snippet view article

partitions of 42 into divisors of 42 1655 = rounded volume of a regular dodecahedron with edge length 6 1656 = 827 + 829: sum of twin prime pair 1657