Search results
Results from the WOW.Com Content Network
The first stellation, often called the stellated rhombic dodecahedron, can be seen as a rhombic dodecahedron with each face augmented by attaching a rhombic-based pyramid to it, with a pyramid height such that the sides lie in the face planes of the neighbouring faces. Luke describes four more stellations: the second and third stellations ...
Rhombic triacontahedron: Compound of great icosahedron and great stellated dodecahedron: Icosidodecahedron: Compound of great icosahedron and great stellated dodecahedron: Great icosidodecahedron: Compound of dodecahedron and icosahedron: Icosidodecahedron: Compound of cube and octahedron: Cuboctahedron: Second stellation of the cuboctahedron ...
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
A regular polyhedral compound can be defined as a compound which, like a regular polyhedron, is vertex-transitive, edge-transitive, and face-transitive.Unlike the case of polyhedra, this is not equivalent to the symmetry group acting transitively on its flags; the compound of two tetrahedra is the only regular compound with that property.
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 ...
The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing.
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.