First stellation of the rhombic dodecahedron information
Self I intersecting polyhedron with 12 faces
Escher's solid. This image does not depict the stellation, because different visible parts of a single hexagonal face of the stellation have different colors. However, the coloring is consistent with a depiction of the polyhedral compound of three flattened octahedra.
STL model of the first stellation of the rhombic dodecahedron decomposed into 12 pyramids and 4 half-cubes
Escher's solid is topologically equivalent to the disdyakis dodecahedron, a Catalan solid, which can be seen as a rhombic dodecahedron with shorter rhombic pyramids augumented to each face.
In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon.
It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual appearance as two other shapes: a solid, Escher's solid, with 48 triangular faces, and a polyhedral compound of three flattened octahedra with 24 overlapping triangular faces.
Escher's solid can tessellate space to form the stellated rhombic dodecahedral honeycomb.
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In geometry, therhombicdodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan...
reduced to zero length, reducing the pentagons into rhombic faces. Therhombicdodecahedron has several stellations, thefirstof which is also a parallelohedral...
as either a polyhedral stellation or a compound. It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed...
considered a stellationofthe cuboctahedron. Generalising Miller's rules there are: 4 stellationsoftherhombicdodecahedron 187 stellationsofthe triakis...
puzzle. stellated rhombicdodecahedron 2×2×2 cube form of Yoshimoto Cube STL model ofthefirststellationoftherhombicdodecahedron decomposed into pyramids...
corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex. Firststellationofrhombicdodecahedron Disdyakis...
both the uniform polyhedra and stellation groupings. back to top back to top back to top List of uniform polyhedra The fifty nine icosahedra List of polyhedral...
In geometry, a rhombic hexecontahedron is a stellationoftherhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry...
constructed by truncating the two axial vertices of a pentagonal trapezohedron. Thestellationsofthe regular dodecahedron make up three ofthe four Kepler–Poinsot...
to each face. Thestellation facets for construction are: Compound of two tetrahedra Compound ofdodecahedron and icosahedron Compound of small stellated...
ofthe Archimedean solids and more particularly, a quasiregular polyhedron. An icosidodecahedron has icosahedral symmetry, and its firststellation is...
dual to the compound of five octahedra. It can be seen as a faceting of a regular dodecahedron. It is one ofthestellationsoftherhombic triacontahedron...
dual to each other. The small stellated dodecahedron and great dodecahedron are dual to each other. The great stellated dodecahedron and great icosahedron...
rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces. Therhombic hexecontahedron is a stellation...
special case of a parallelepiped, and therhombicdodecahedron (with five stellations per Miller's rules) is the only Catalan solid to tessellate space...
obtained as stellationsofthedodecahedron and the icosahedron. The next most regular convex polyhedra after the Platonic solids are the cuboctahedron...
polyhedron is therhombicdodecahedron. The cuboctahedron was probably known to Plato: Heron's Definitiones quotes Archimedes as saying that Plato knew of a solid...
The compound of five octahedra is one ofthe five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund...
removing the pentagonal pyramids. The regular icosahedron has many relations with other Platonic solids, one of them is the regular dodecahedron as its...
into the study of polyhedra. The Kepler–Poinsot polyhedra may be constructed from the Platonic solids by a process called stellation. Most stellations are...
The stellated octahedron is the only stellationofthe octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given...
cuboctahedron and the icosidodecahedron; and two Catalan solids: therhombicdodecahedron and therhombic triacontahedron, which are duals to the only two quasiregular...
chronologically): 1963-69 Stellated RhombicDodecahedron Puzzle The Mathematics Teacher (March 1963). The World of Polyhedrons The Mathematics Teacher (March 1965)...
{n/(n − m)}) and m and n are coprime (as such, all stellationsof a polygon with a prime number of sides will be regular stars). Symbols where m and n...
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