The Concept of Elevation applied to Flat Tiling Patterns

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Rinus Roelofs: The Concept of Elevation applied to Flat Tiling Patterns. In: Bridges 2015. Pages 9–16



In their book “La Divina Proportione”, Luca Pacioli and Leonardo da Vinci described and illustrated an operation which you can apply to a polyhedron, called Elevation. In this paper I want to show how you can make models of these elevations from simple elements, material that can be used for workshops. Luca Pacioli and Leonardo da Vinci applied the elevation operation only to polyhedra, but the concept can also be applied at 2D tiling patterns, resulting in interesting single and double weaving patterns.

Extended Abstract


 author      = {Rinus Roelofs},
 title       = {The Concept of Elevation applied to Flat Tiling Patterns},
 pages       = {9--16},
 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] Luca Pacioli – Leonardo da Vinci, La Divina Proportione, 1509, Ed. Akal, S.A., Madrid, 1991

[2] Rinus Roelofs, Elevations and Stellations, Bridges Proceedings, Seoul, 2014.

[3] Luca Pacioli, Divina Proportione: Die Lehre Vom Goldenen Schnitt, 1509, Ed. Carl Graeser, Wien, 1896.

[4] B. Grünbaum – G.C. Shephard, Tilings and Patterns, W.H. Freeman and Company, New York, 1987.


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