# Year: 2013

## Periodic Modification of the Boerdijk-Coxeter Helix (Tetrahelix)

The Boerdijk-Coxeter helix is a helical structure of tetrahedra which possesses no non-trivial translational or rotational symmetries. In this document, we develop a procedure by which this structure is modiﬁed to obtain both translational and rotational (upon projection) symmetries along/about its central axis. We report the ﬁnding of several, distinct periodic structures, and focus on […]

## Cabinet of Curiosities: The Interesting Geometry of the Angle β = arccos((3φ – 1)/4)

In this paper, we present the construction of several aggregates of tetrahedra. Each construction is obtained by performing rotations on an initial set of tetrahedra that either (1) contains gaps between adjacent tetrahedra, or (2) exhibits an aperiodic nature. Following this rotation, gaps of the former case are “closed” (in the sense that faces of […]

## Law of Sums of the Squares of Areas, Volumes and Hyper Volumes of Regular Polytopes from Clifford Polyvectors

Inspired by the Sum of the Squares law obtained in the paper titled “The Sum of Squares Law” by J. Kovacs, F. Fang, G. Sadler and K. Irwin, we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in […]