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The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (±1, ±1, ±1) and (0, 1 + h, 1 − h 2) with parameter h = 1. These coordinates illustrate that a rhombic dodecahedron can be seen as a cube with six square pyramids attached to each face, allowing them to fit together into a ...
The trapezo-rhombic dodecahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It consists of copies of a single cell, the trapezo-rhombic dodecahedron. It is similar to the higher symmetric rhombic dodecahedral honeycomb which has all 12 faces as rhombi.
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 ...
rhombic triacontahedron: 2|3 5 3.5.3.5 I h: U24 K29 30 60 32 ... (Third stellation of dodecahedron) I h: Stellations of icosahedron. Index Name Symmetry group
Here we usually add the rule that all of the original face planes must be present in the stellation, i.e. we do not consider partial stellations. For example the cube is not usually considered a stellation of the cuboctahedron. Generalising Miller's rules there are: 4 stellations of the rhombic dodecahedron; 187 stellations of the triakis ...
It has octahedral symmetry (O h) and shares the same vertices as a rhombic dodecahedron. This can be seen as the three-dimensional equivalent of the compound of two squares ({8/2} " octagram "); this series continues on to infinity, with the four-dimensional equivalent being the compound of tesseract and 16-cell.
The rhombic dodecahedron, generated from four line segments, no two of which are parallel to a common plane. Its most symmetric form is generated by the four long diagonals of a cube. [2] It tiles space to form the rhombic dodecahedral honeycomb. The elongated dodecahedron, generated from five line segments, with two triples of coplanar segments.
A stellation diagram, or facetting diagram, (for polyhedra) represents facet plane intersections outside of a uniform polyhedra face. The inner most polygon represents the original face. The inner most polygon represents the original face.