4D Euclidean space

News Archive

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September 2018

This month, we continue our exploration of octa-augmented polychora, CRF polytopes produced by augmenting members of the tesseract family of uniform polychora along their axial symmetries.

The octa-augmented runcitruncated 16-cell

This is the octa-augmented runcitruncated 16-cell, a beautiful polytope that sports 24 elongated square bipyramids (J15) as cells, among other shapes. It can also be considered as one of the partial Stott contractions of the runcitruncated 24-cell, or a Stott expansion of the octa-augmented runcinated tesseract.

Learn more about this polychoron at the octa-augmented runcitruncated 16-cell page. As usual, we provide the full Cartesian coordinates.

August 2018

This month, we present the octa-augmented truncated tesseract:

The octa-augmented truncated tesseract

This is a CRF polytope that sports 24 square orthobicupolae (J28) as cells, in addition to 8 cuboctahedra, 64 triangular prisms, and 16 tetrahedra. It can be considered as a partial Stott expansion of the 24-cell according to its subsymmetry as an octa-augmented tesseract (as opposed to full 24-cell symmetry).

It is, obviously, related to last month's Polytope of the Month, the octa-augmented runcinated tesseract, except that it has square orthobicupolae where the latter has elongated square bipyramids.

Find out more on the octa-augmented truncated tesseract page. As usual, the full coordinates are included.

July 2018

This month, we introduce an interesting CRF polytope that sports elongated square bipyramids (J15) as cells. This is the octa-augmented runcinated tesseract:

The octa-augmented runcinated tesseract

It has 72 vertices, 256 edges, 256 polygons, and 72 cells (including 24 elongated square bipyramids), and is related to the 24-cell as a modified partial Stott expansion, besides being an augmentation of the runcinated tesseract.

So go on over to the octa-augmented runcinated tesseract page to learn more about the structure of this interesting polychoron. As is customary, we provide full Cartesian coordinates.

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Last updated 16 Jan 2019.

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