Obtaining the H and T Honeycomb from a Cross-Section of the 16-cell Honeycomb

Hideki Tsuiki
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 147–152 Regular Papers


The two polyhedra H (Hexagonal bipyramid imaginary cube) and T (Triangular antiprismoid imaginary cube) form a honeycomb (3D tiling) which is obtained by truncating vertices of the cubic honeycomb, and at the same time, is obtained by truncating vertices of a honeycomb of triangular prisms. In this paper, we show that this honeycomb is obtained by shrinking a cross-section of the 4-dimensional honeycomb of 16-cells.