Deltoidal icositetrahedron
In the image above, the long body diagonals are those between opposite red vertices and between opposite blue vertices, and the short body diagonals are those between opposite yellow vertices.Cartesian coordinates for the vertices of the deltoidal icositetrahedron centered at the origin and with long body diagonal length 2 are: Where
A deltoidal icositetrahedron has three regular-octagon equators, lying in three orthogonal planes.
The deltoidal icositetrahedron with long body diagonal length D = 2 has:
Specifically, the side adjacent to the obtuse angle has a length of approximately 0.707106785, while the side adjacent to the acute angle has a length of approximately 0.914213565.
The deltoidal icositetrahedron is a crystal habit often formed by the mineral analcime and occasionally garnet.
3, the device containing the files about the experiments carried on Rocket Raccoon has the shape of a deltoidal icositetrahedron.
The deltoidal icositetrahedron has three symmetry positions, all centered on vertices: The deltoidal icositetrahedron's projection onto a cube divides its squares into quadrants.
The projection onto a regular octahedron divides its equilateral triangles into kite faces.
In Conway polyhedron notation this represents an ortho operation to a cube or octahedron.
A variant with pyritohedral symmetry is called a dyakis dodecahedron[5][6] or diploid.
A tetartoid can be created by enlarging 12 of the 24 faces of a dyakis dodecahedron.
[8] The great triakis octahedron is a stellation of the deltoidal icositetrahedron.
The deltoidal icositetrahedron is a member of a family of duals to the uniform polyhedra related to the cube and regular octahedron.
In that case the resulting icositetrahedron will no longer have a rhombicuboctahedron for a dual, since the centers of the square and triangle faces of a rhombicuboctahedron are at different distances from its center.
This polyhedron is a term of a sequence of topologically related deltoidal polyhedra with face configuration V3.4.n.4; this sequence continues with tilings of the Euclidean and hyperbolic planes.
