Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids
Inhaltsverzeichnis
Reference
David A. Reimann: Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids. In: Bridges 2015. Pages 143–150
DOI
Abstract
The process of replacing each edge of a regular polyhedron with a square results in the creation of a new object, similar to the process of Stott expansion. However, following the edge to square transformation, the resulting object's surface no longer has genus zero. In some cases, the object also contains bumps or craters to accommodate the additional length of material. This process can be generalized to any polyhedral form having equal length edges, such as Platonic solids, Archimedean solids, prisms, and anti-prisms. Examples are shown for these particular classes of polyhedra using a variety of materials and symmetries.
Extended Abstract
Bibtex
@inproceedings{bridges2015:143,
author = {David A. Reimann},
title = {Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids},
pages = {143--150},
booktitle = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
year = {2015},
editor = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
isbn = {978-1-938664-15-1},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-143.html}}
}
Used References
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Links
Full Text
http://archive.bridgesmathart.org/2015/bridges2015-143.pdf
