Tessellations from Group Actions and the Mystery of Escher’s Solid

Year: 2005 Authors: Ioana Mihaila

Core claim

Successive tessellations obtained by dissecting tiles correspond to subgroup chains of index 2 in the associated translation groups.

Topics

tessellations, group actions, space-filling polyhedra, Escher’s solid

Domains

group theory, geometric tessellations, 3D symmetry, mathematical art, visual geometry, architectural patterning

Methods

cut-and-attach construction, checkerboard subdivision, iterated dissection, group-action description

Media

unit squares, cubes, rhombic dodecahedra, stellated rhombic dodecahedron

Source status

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