Ingrid Daubechies

Artists

Ingrid Daubechies

Professor of Mathematics

Duke University

Durham, North Carolina, USA

ingrid@math.duke.edu

Statement

I have long admired the pieces submitted to the JMM art exhibits, and longed to be able to participate. Through my involvement in the collaborative Mathemalchemy project (see mathemalchemy.org), I practiced many craft techniques, and overcame my threshold fear. In particular I learned temari embroidery, a Japanese craft in which balls are wrapped in many layers of thread that cover the surface completely, and that are then embroidered in contrasting colors. My temari balls are typically quite geometric. Some of them are now used by my husband for demonstrations in his Algebra class.

Artworks

Image for entry 'Twelve stars -- five cubes' — Twelve stars -- five cubes
10.0 x 25.0 x 20.0 cm
scrap fabric and paper (for the core), thread (wrapping and embroidery)
2023

Connecting all the non-adjacent vertices on each pentagonal face of a dodecahedron gives rise to five-pointed stars touching at their tips; this also gives the edges of 5 cubes. This illustrates that the tetrahedral symmetry group (symmetries of the tetrahedron) is a subgroup of the icosahedral symmetry group (symmetries of the dodecahedron) as well as of the octahedral symmetry group (symmetries of the cube). In the icosahedral group, the tetrahedral (sub)group has 4 other cosets (hence the five cubes); in the octahedral group, the tetrahedral (sub)group consists of those symmetries of the cube that fix each of the two tetrahedra embedded in the cube -- the only symmetries of the 5 nestled cubes that also fix the whole dodecahedron.

Ingrid Daubechies

Artists