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Symmetry 2012, 4(4), 644-666; doi:10.3390/sym4040644

A Peculiarly Cerebroid Convex Zygo-Dodecahedron is an Axiomatically Balanced “House of Blues”: The Circle of Fifths to the Circle of Willis to Cadherin Cadenzas

Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA
Received: 24 August 2012 / Revised: 28 October 2012 / Accepted: 6 November 2012 / Published: 15 November 2012
(This article belongs to the Special Issue Polyhedra)

Abstract

A bilaterally symmetrical convex dodecahedron consisting of twelve quadrilateral faces is derived from the icosahedron via a process akin to Fuller’s Jitterbug Transformation. The unusual zygomorphic dodecahedron so obtained is shown to harbor a bilaterally symmetrical jazz/blues harmonic code on its twelve faces that is related to such fundamental music theoretical constructs as the Circle of Fifths and Euler’s tonnetz. Curiously, the patterning within the aforementioned zygo-dodecahedron is discernibly similar to that observed in a ventral view of the human brain. Moreover, this same pattern is arguably evident during development of the embryonic pharynx. A possible role for the featured zygo-dodecahedron in cephalogenesis is considered. Recent studies concerning type II cadherins, an important class of proteins that promote cell adhesion, have generated data that is demonstrated to conform to this zygo-dodecahedral brain model in a substantially congruous manner.
Keywords: bilateral symmetry; geometrical music theory; dodecahedra; morphogenesis; cephalogenesis; cadherins; brain networks bilateral symmetry; geometrical music theory; dodecahedra; morphogenesis; cephalogenesis; cadherins; brain networks
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Becker, D.A. A Peculiarly Cerebroid Convex Zygo-Dodecahedron is an Axiomatically Balanced “House of Blues”: The Circle of Fifths to the Circle of Willis to Cadherin Cadenzas. Symmetry 2012, 4, 644-666.

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