XXX Rhombicosidodecahedron - Wikipedia Bilder
Johannes Kepler in Harmonices Mundi named this Ece Yasar a rhombicosidodecahedronbeing short for truncated icosidodecahedral rhombuswith icosidodecahedral rhombus being his name for a rhombic triacontahedron.
It can also be called an expanded or cantellated dodecahedron or icosahedron, from truncation operations on either uniform polyhedron. If you expand an icosahedron by moving the faces away Rhombidodecahedron the origin the right amount, without changing the orientation or size of the faces, and do the same to its dual dodecahedronand patch the square holes in the result, you get a rhombicosidodecahedron. Two clusters of faces of the bilunabirotundathe lunes each lune featuring two triangles adjacent to opposite sides of one squarecan be aligned with a congruent patch Rhombidodecahedron faces on Rhombidodecahedron rhombicosidodecahedron.
If two bilunabirotundae are aligned this way on opposite sides of the rhombicosidodecahedron, then a cube can be put between the bilunabirotundae at the very center of the rhombicosidodecahedron. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors.
The balls are "expanded" rhombicosidodecahedra, with the squares replaced by rectangles. The expansion is chosen so that the resulting rectangles are golden rectangles.
Cartesian coordinates for the vertices of a rhombicosidodecahedron with an edge length Rhombidodecahedron 2 centered at the origin are all even permutations of: . For unit edge length, R must be halved, giving. The last two correspond to the A 2 and H 2 Coxeter planes. The rhombicosidodecahedron can also be represented as a spherical tiling Facetime Sex, and projected onto the plane via a stereographic projection.
This projection is conformalpreserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. This polyhedron is topologically related as a part of a sequence Rhombidodecahedron cantellated polyhedra with vertex figure 3. There are 13 related Johnson solids5 Aleksa Slusarchi diminishment, and 8 including gyrations:.
In the mathematical field of graph theorya rhombicosidodecahedral graph is the graph of vertices and edges of the rhombicosidodecahedron, one of the Archimedean solids. It has 60 vertices and edges, and is a quartic graph Archimedean graph. From Wikipedia, the free encyclopedia. Archimedean solid. Orthogonal projections in Geometria by Augustin Hirschvogel. AitonA.
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Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Wikimedia Commons. Rhombidodecahedron here for rotating model. Archimedean solid Uniform polyhedron. Conway notation. Schläfli symbols. Wythoff symbol. Coxeter diagram. Symmetry group. Rotation group. Dihedral angle. Semiregular convex. Colored faces. Deltoidal hexecontahedron dual polyhedron. Triangle -centered.
Square -centered. Small dodecicosidodecahedron. Small rhombidodecahedron. Small stellated truncated dodecahedron. Quartic graphHamiltonianregular. Table of graphs and parameters. Truncated tetrahedron Truncate.
Truncated tetrahedron Zip. Truncated cube Truncate. Truncated octahedron Zip. Truncated dodecahedron Rhombidodecahedron. Truncated icosahedron Zip. Tetratetrahedron Ambo. Cuboctahedron Ambo. Icosidodecahedron Rhombidodecahedron. Rhombitetratetrahedron Expand.
Truncated tetratetrahedron Bevel. Rhombicuboctahedron Expand. Truncated cuboctahedron Bevel. Rhombicosidodecahedron Expand. Truncated icosidodecahedron Bevel. Snub tetrahedron Snub. Snub cube Snub. Snub dodecahedron Snub. Catalan duals Triakis tetrahedron Needle. Triakis tetrahedron Kis. Triakis octahedron Needle. Tetrakis hexahedron Kis. Triakis icosahedron Needle.
Pentakis dodecahedron Kis. Rhombic hexahedron Join. Eroric Images dodecahedron Join.
Rhombic Rhombidodecahedron Join. Deltoidal dodecahedron Ortho. Disdyakis hexahedron Meta. Deltoidal icositetrahedron Ortho. Disdyakis dodecahedron Meta. Deltoidal hexecontahedron Ortho. Disdyakis triacontahedron Meta.
Johannes Kepler in Harmonices Mundi named this polyhedron a rhombicosidodecahedron , being short for truncated icosidodecahedral rhombus , with icosidodecahedral rhombus being his name for a rhombic triacontahedron. It can also be called an expanded or cantellated dodecahedron or icosahedron, from truncation operations on either uniform polyhedron.
The (first) rhombic dodecahedron is the dual polyhedron of the cuboctahedron A_1 (Holden , p. 55) and Wenninger dual W_(11). Its sometimes also called the rhomboidal dodecahedron (Cotton ), and the "first" may be included when needed to distinguish it from the Bilinski dodecahedron (Bilinski , Chilton and Coxeter ). A rhombic dodecahedron appears in the upper right as one of.
The rhombic dodecahedron (hereinafter, referred to as r.d.) is a semi-regular polyhedron, in that all of its edges are the same length, yet the angles of its faces differ. Because each face is a parallelogram, there are 2 distinct angles for each face, one which is bisected by the long axis, with an angle less than 90 degrees, the other bisected by the short axis, with an angle greater than
In geometry , the small rhombidodecahedron is a nonconvex uniform polyhedron , indexed as U It has 42 faces 30 squares and 12 decagons , edges, and 60 vertices. It additionally shares its edge arrangement with the rhombicosidodecahedron having the square faces in common , and with the small dodecicosidodecahedron having the decagonal faces in common. The small rhombidodecacron or small dipteral ditriacontahedron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.