## Journal of Symplectic Geometry

### The Symplectic Geometry of Penrose Rhombus Tilings

#### Abstract

The purpose of this article is to view Penrose rhombus tilings from the perspective of symplectic geometry. We show that each thick rhombus in such a tiling can be naturally associated to a highly singular 4-dimensional compact symplectic space $M_R$, while each thin rhombus can be associated to another such space $M_r$; both spaces are invariant under the Hamiltonian action of a 2-dimensional quasitorus, and the images of the corresponding moment mappings give the rhombuses back. The spaces $M_R$ and $M_r$ are diﬀeomorphic but not symplectomorphic.

#### Article information

Source
J. Symplectic Geom., Volume 6, Number 2 (2008), 139-158.

Dates
First available in Project Euclid: 27 August 2008

https://projecteuclid.org/euclid.jsg/1219866510

Mathematical Reviews number (MathSciNet)
MR2434438

Zentralblatt MATH identifier
1159.52021

#### Citation

Battaglia, Fiammetta; Prato, Elisa. The Symplectic Geometry of Penrose Rhombus Tilings. J. Symplectic Geom. 6 (2008), no. 2, 139--158. https://projecteuclid.org/euclid.jsg/1219866510