Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


David A. Reimann: Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids. In: Bridges 2015. Pages 143–150



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


 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{ }},
 url         = { },

Used References

[1] Johannes Kepler. The harmony of the world. American Philosophical Society, 209, 1997. Translated into English with an Introduction and Notes by E.J. Aiton, A.M. Duncan, and J.V. Field.

[2] Makedo. Giant windball., Accessed 1/31/2015.

[3] Yoshinobu Miyamoto. Square unit spheres., Accessed 1/31/2015.

[4] Irene Polo-Blanco. Alicia boole stott, a geometer in higher dimension. Historia Mathematica, 35(2):123–139, 2008.

[5] Eric W. Weisstein. Expansion. From MathWorld—A Wolfram Web Resource., Accessed 1/31/2015.

[6] Junichi Yananose. Juno’s spinner truncated icosahedron. In Reza Sarhangi and Carlo H. S´equin, editors, Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, pages 461–462, 2008.


Full Text

intern file

Sonstige Links