17 citations · 135 across the 31 of their papers we have counts for
4 papers · 1 filter
An Icosahedral Quasicrystal as a Golden Modification of the Icosagrid and its Connection to the E8 Lattice
Fang Fang, Klee Irwin
We present an icosahedral quasicrystal as a modification of the icosagrid, a multigrid with 10 plane sets that are arranged with icosahedral symmetry. We use the Fibonacci chain to…
Cabinet of curiosities: the interesting geometry of the angle β = arccos((3ϕ - 1)/4)
Fang Fang, Klee Irwin, Julio Kovacs +1
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)…
Periodic modification of the Boerdijk-Coxeter helix (tetrahelix)
Garrett Sadler, Fang Fang, Julio Kovacs +1
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 w…
The Sum of Squares Law
Julio Kovacs, Fang Fang, Garrett Sadler +1
We show that when projecting an edge-transitive N-dimensional polytope onto anM-dimensional subspace of R^N, the sums of the squares of the original and projected edges are in the…