The dual to that truncation will be the triakis truncated tetrahedron.

The truncated 5-cell is the 4-dimensional analogue of the truncated tetrahedron.

But there are four more structures within that, the innermost being a truncated tetrahedron of 12 oxygen atoms.

In geometry, the truncated tetrahedron is an Archimedean solid.

Its dual is the truncated tetrahedron.

The projection envelope is a truncated tetrahedron.

For space-filling, the triakis truncated tetrahedron can be constructed as follows:

In geometry, the augmented truncated tetrahedron is one of the Johnson solids (J).

It is created by attaching a triangular cupola to one hexagonal face of an truncated tetrahedron.

The area A and the volume V of a truncated tetrahedron of edge length a are:

A truncated tetrahedron, with a floorspace of 20 square metres, the Spaceframe requires no foundations and can be assembled by hand.

The truncated tetrahedron first parallel projection of the truncated 16-cell into 3-dimensional space has the following structure:

A lower symmetry version of the truncated tetrahedron is called a Friauf polyhedron in crystals such as complex metallic alloys.

Each hexagonal face of the truncated tetrahedra is joined in complementary orientation to the neighboring truncated tetrahedron.

In geometry, the triakis truncated tetrahedron is a convex polyhedron made from 4 hexagons and 12 isoceles triangles.

Polyhedral models with tetrahedral symmetry most often have convex hull a truncated tetrahedron - see and for examples and illustrations.

Each vertex is surrounded by 2 truncated octahedra, one triangular prism, and one truncated tetrahedron.

J: Augmented truncated tetrahedron (8 equilateral triangles, 3 squares, 3 regular hexagons)

The triakis truncated tetrahedron is the shape of the Brillouin zone of the carbon atoms in diamond, which lie on the diamond cubic crystal structure.

In fact, if the truncation of the corners is slightly smaller than that of an Archimedean truncated tetrahedron, this new shape can be used to completely fill space.

This layout of cells in projection is analogous to the layout of faces in the face-first projection of the truncated tetrahedron into 2-dimensional space.

If all of a triakis tetrahedron's vertices, of both kinds, are truncated, the resulting solid is an irregular icosahedron, whose dual is a trihexakis truncated tetrahedron.

Each vertex is surrounded by five cells: one truncated tetrahedron, two hexagonal prisms, one triangular prism, and one cuboctahedron; the vertex figure is a rectangular pyramid.

Meffert also produces a similar puzzle called the Tetraminx, which is the same as the Pyraminx except that the trivial tips are removed, turning the puzzle into a truncated tetrahedron.

Cartesian coordinates for the 12 vertices of a truncated tetrahedron centered at the origin, with edge length 8, are all permutations of ( 1, 1, 3) with an even number of minus signs: