Octahedron atop Rhombicuboctahedron


Octahedron atop rhombicuboctahedron (octahedron || rhombicuboctahedron), or K4.107 among Dr. Richard Klitzing's segmentochora, is a 4D CRF polytope that consists of an octahedron and a rhombicuboctahedron in parallel hyperplanes, connected to each other by 20 triangular prisms and 6 square pyramids.

K4.107: Octahedron
atop Rhombicuboctahedron

Eight copies of K4.107 can be attached to the runcitruncated 16-cell to form the octa-augmented runcitruncated 16-cell, in which the square pyramids of K4.107 and the cubes of the runcitruncated 16-cell lie in coincident hyperplanes and thus merge into elongated square bipyramids (J15).

Structure

The structure of K4.107 is quite simple. We shall explore it using its parallel projections into 3D:

Parallel projection of
K4.107, showing octahedral cell

The above image shows the octahedral cell of K4.107. It lies closest to this 4D viewpoint.

The next image shows 8 of the triangular prisms that are attached to this octahedron:

Parallel projection of
K4.107, showing 8 triangular prisms

Between these triangular prisms are more triangular prisms, another 12 of them:

Parallel projection of
K4.107, showing 12 more triangular prisms

The remaining gaps are filled by 6 square pyramids:

Parallel projection of
K4.107, showing 12 more triangular prisms

Finally, the last cell is the antipodal rhombicuboctahedron:

Parallel projection of
K4.107, showing antipodal rhombicuboctahedron

For clarity, we have omitted the other cells that have already been shown.

Coordinates

The Cartesian coordinates of K4.107 with edge length 2 are:


Last updated 01 Sep 2018.

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