TL;DR
This paper explores minimal 7-fold rhombic tilings using a substitution scheme with 11 proto-rhombs, revealing new tilings and the role of the 7-fold magic number phi in their structure.
Contribution
It introduces a minimal set of proto-rhombs for 7-fold tilings and derives the general substitution form involving the magic number phi.
Findings
Discovered a minimal set of proto-rhombs for 7-fold tilings
Derived the general form of 7-fold substitution schemes
Presented new 7-fold tilings with detailed figures
Abstract
A study of 7-fold tilings that use a set of three proto-rhombs in a substitution scheme to tile a large area. A set is discovered that is thought to be the most minimal or smallest one. The scheme uses 11 proto-rhombs to tile the next generation of inflated tiles. The general form of 7-fold substitutions is shown and the role of the 7-fold magic number phi is derived. The figures include a number of newly discovered 7-fold tilings.
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Taxonomy
TopicsQuasicrystal Structures and Properties