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...

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

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

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...

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...

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

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

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...

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

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

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...

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

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

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...

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...

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...

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...

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...

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...

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...

lobby; it depicts the compound of five tetrahedra as five interlocked aluminum shapes, inspired by an origami version of the same compound folded by Tom Hull...

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

with concave pentagonal pyramids in place of its faces. Its exterior surface represents the Ef1g1 stellation of the icosahedron. It appears in Magnus Wenninger's...

rule, the internal structure of both shapes will differ. The 12 vertices of the convex hull matches the vertex arrangement of an icosahedron. The great triambic...

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...

diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence. The great icosahedron...

geometry of three dimensions, a stellation extends a polyhedron to form a new figure that is also a polyhedron. The following is a list of stellations of various...

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

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