The compound of five tetrahedra is one of the five regular polyhedral compounds. This compound polyhedron is also a stellation of the regular icosahedron...

The compound of ten tetrahedra is one of the five regular polyhedral compounds. This polyhedron can be seen as either a stellation of the icosahedron...

The compound of five truncated tetrahedra is a uniform polyhedron compound. It's composed of 5 truncated tetrahedra rotated around a common axis. It may...

only regular compound with that property. There are five regular compounds of polyhedra: Best known is the regular compound of two tetrahedra, often called...

compound of tetrahedra might be: Compound of two tetrahedra – stellated octahedron Compound of three tetrahedra Compound of four tetrahedra Compound of...

compound of four tetrahedra can be constructed by four tetrahedra in a number of different symmetry positions. A uniform compound of four tetrahedra can...

The compound of five octahedra is one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund...

of regular polyhedra and tilings with order-3 vertex figures. Compounds of tetrahedra Two tetrahedra in a cube Compound of five tetrahedra Compound of...

rhombidodecadodecahedron. The compound of ten tetrahedra can be formed by taking each of these five cubes and replacing them with the two tetrahedra of the stella octangula...

overlapping tetrahedra. This can be generalized to any desired amount of higher dimensions; the four-dimensional equivalent construction is the compound of two...

showing many stellations and facetings of polyhedra. In 1619, Kepler described a regular compound of two tetrahedra which fits inside a cube, and which he...

forming a compound of ten tetrahedra. Further, we can choose one tetrahedron from each stella octangula, so as to derive a compound of five tetrahedra, which...

rhombihexahedra Compound of five small stellated dodecahedra Compound of five stellated truncated cubes Compound of five tetrahedra Compound of five tetrahemihexahedra...

them. Other stellations have more than one face in each plane or form compounds of simpler polyhedra. These are not strictly icosahedra, although they are...

In mathematics, a group action of a group G {\displaystyle G} on a set S {\displaystyle S} is a group homomorphism from G {\displaystyle G} to some group...

only five polyhedral compounds (along with the compound of six tetrahedra, the compound of two great dodecahedra, the compound of two small stellated dodecahedra...

rhombihexahedra Compound of five small stellated dodecahedra Compound of five stellated truncated cubes Compound of five tetrahedra Compound of five tetrahemihexahedra...

group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of degree n, or the...

is a compound of five 600-cells (in two ways), the dodecahedron is a compound of five regular tetrahedra (in two ways). As two opposing tetrahedra can...

Dehn invariant, except for the two tetrahedra whose Dehn invariants were different. The cube has a Dehn invariant of zero. This indicates the cube is applied...

The compound of six tetrahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 6 tetrahedra. It can be constructed by inscribing...

centrally symmetric). It acts on the compound of ten tetrahedra: I acts on the two chiral halves (compounds of five tetrahedra), and −1 interchanges the two...

realized as the geometries of polyhedra (equivalently, tilings of Riemann surfaces), respectively: the compound of five tetrahedra inside the icosahedron...

loosely seen as the two-dimensional equivalent of the 3D compound of five tetrahedra. Deeper truncations of the regular pentadecagon and pentadecagrams can...

polytope has six hundred regular tetrahedra as its cells. Dice are the most common objects using different polyhedra, one of them being the regular icosahedron...

transitive embedding of S5 into S6 produces another pair of five-dimensional irreducible representations. The representation theory of the alternating groups...

sharing the same face planes, the compound of six tetrahedra, may be formed by stellating each face of the compound of three octahedra to form three stellae...

made up of four intersecting triangles. Compound of five tetrahedra Compound of ten tetrahedra Sloane, N. J. A. (ed.). "Sequence A119602 (Number of nonisomorphic...

final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in...

PSL(2,5) is the symmetries of the icosahedron (genus 0) with the compound of five tetrahedra as a 5-element set, PSL(2,7) of the Klein quartic (genus 3)...