Tetrahedra in a sentence

Inscribing tetrahedra inside the regular compound of five cubes gives two more regular compounds, containing five and ten tetrahedra.

The complete list remains an open problem. citation If one relaxes the requirement that the tetrahedra be all the same shape, one can tile space using only tetrahedra in many different ways.

The compound of five tetrahedra comes in two enantiomorphic versions, which together make up the compound of 10 tetrahedra.

At the next iteration, the side-length is halved: : and there are 4 such smaller tetrahedra.

BeCl 2 and BeBr 2 have chain structures with edge-shared tetrahedra.

Cleavage is not a universal property among minerals; for example, quartz, consisting of extensively interconnected silica tetrahedra, does not have a crystallographic weakness which would allow it to cleave.

Correspondingly, a regular octahedron is the result of cutting off from a regular tetrahedron, four regular tetrahedra of half the linear size (i.e. rectifying the tetrahedron).

Disilicates (or sorosilicates) have two tetrahedra sharing one oxygen atom.

Dyar and Gunter, p. 105 Orthosilicates (or nesosilicates) have no linking of polyhedra, thus tetrahedra share no corners.

Five tetrahedra are laid flat on a plane, with the highest 3-dimensional points marked as 1, 2, 3, 4, and 5. These points are then attached to each other and a thin volume of empty space is left, where the five edge angles do not quite meet.

For example, one can divide an octahedron into four identical tetrahedra and combine them again with two regular ones.

Framework silicates, or tectosilicates, have tetrahedra that share all four corners.

Fuller wrote that the natural analytic geometry of the universe was based on arrays of tetrahedra.

He showed that the figure-eight knot complement could be decomposed as the union of two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched up correctly and gave the hyperbolic structure on the figure-eight knot complement.

However, two regular tetrahedra can be combined with an octahedron, giving a rhombohedron that can tile space.

In contrast, micas, which have perfect basal cleavage, consist of sheets of silica tetrahedra which are very weakly held together.

In different minerals the tetrahedra show different degrees of networking and polymerization.

In fact, five is the minimum number of tetrahedra required to compose a cube.

Isometries of irregular tetrahedra The isometries of an irregular (unmarked) tetrahedron depend on the geometry of the tetrahedron, with 7 cases possible.

Metallotropic liquid crystals Liquid crystal phases can also be based on low-melting inorganic phases like ZnCl 2 that have a structure formed of linked tetrahedra and easily form glasses.