Last edited 4may17 by gfrancis@illinois.edu

## Stability of Quasicrystal Frameworks Projects 2017

Illinois Graphics Lab (IGL)

Mathematics Department, U Illinois, Urbana

The IGL project series on the
stability of quasicrystal frameworks
began in
2014 with the completion of a proof of Wester's Conjecture in 2D, illustrated
by the
Wester Game.
It was continued the following year with progress on a
3D generalization,
culminating in conjectures supported by experimental
software, but only for special cases of the crystalline structures (rectangular
clusters of cubical cells) and restricted deformations (those that preserve
the planarity of the faces of the the rhombic hexahedral "brick").
This 2017, two groups of five students, each worked on building software
for further explore the 3D problem in particular the case of general
Penrose quasicrystalline clusters and some progress on the most general
case that the deformation group includes twists and asymmetric shears of
(still) cubical frameworks.

The elementary group learned the rudiments of programming real-time interative
computer animations (RTICA) in Python/TkInter, Python/OpenGL, and
Javascript/HTML5/CANVAS.

Members of the advanced group made significant
progress in four areas of the general problem to be solved.
Sasha Lamtyugina continued the work of earlier students
by re-implementing the
DeBruijn-Robbin generator of 3D quasicrystal
clusters into Python/OpenGL. This software was originally
programmed in Schaeffer-Crowell's Syzygy, which is the distributed graphics
software for the virtual environments (CAVE, Cube, Oculus Rift) of
the (now destroyed) Illinois Simulation Laboratory (ISL) of the
Beckman Institute.
Yijing Chen implemented the three
projection panels for the testing of the Duarte-Francis Shadow Conjecture
generaliziging their proof of the 2D-Wester Conjecture.
Arturo Guerrero worked of the shift deformations
for the stratification of arbirtrary rhomboid (Penrose) clusters, generalizing
the Baglivo-Garver (cubical crystalline framework) shifts. And
Zachary Berrebah explored the conjectured elementary generators
of the deformations of a cubical framemework in 3D.

### Stability of Quasicrystals, Elementary Group

Lisa and Manting: AllertonJS

Pranav: Two Octahedra

SungJib: Linked Tori

Two Skinny Bricks Tejo13
### Stability of Quasicrystals, Advanced Group

Yijing: ShadowConjecture

Arturo : 10_bricks.html

Arturo: 4_bricks.html

Arturo: triacontahedron