Forming the Cupolae With Concave Polyhedral Surfaces by Corrugating a Fourfold Strip of Equilateral Triangles
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Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)
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The cupolae with concave polyhedral surfaces consist of: two regular
polygons, n-gone and 2n-gone in parallel planes, interconnected by an
envelope constituted of series of equilateral triangles. The paper
describes cupolae which originate by corrugating of a fourfold strip of
equilateral triangles, forming thereby the envelope of a cupola. In
this manner, a non-convex polyhedron is emerged. Such a method of corrugating the envelope, allows the solutions for generating cupolae with base polygon which number of sides exceedes n=10, which was the maximal number of sides for cupole with the envelope consisted of twofold strip of equilateral triangles. By analyzing the elements of these polyhedra and by help of their paper models, we find geometric constructions and projection procedures by which it is possible to graphically display the cupolae.
Keywords:
cupola / concave polyhedral surface / envelope / modelSource:
PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010, 2010, 363-374Publisher:
- Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)
Funding / projects:
- Primena rezultata naprednog razvoja prostornih struktura u oblasti 3D transformacija, konstruisanja, novih materijala - Simprolita i tehnologija (RS-MESTD-MPN2006-2010-16009)
Note:
- http://mongeometrija.com/media/mongeometrija/2010/moNGeometrija%202010%20-%20PAGINACIJA.pdf http://mongeometrija.com/component/content/article/52-slobodan-mii/115-misic-obradovic-forming-the-cupolae-with-concave-polyhedral-surfaces-by-corrugating-a-fourfold-st
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GraFarTY - CONF AU - Mišić, Slobodan AU - Obradović, Marija PY - 2010 UR - https://grafar.grf.bg.ac.rs/handle/123456789/2047 AB - The cupolae with concave polyhedral surfaces consist of: two regular polygons, n-gone and 2n-gone in parallel planes, interconnected by an envelope constituted of series of equilateral triangles. The paper describes cupolae which originate by corrugating of a fourfold strip of equilateral triangles, forming thereby the envelope of a cupola. In this manner, a non-convex polyhedron is emerged. Such a method of corrugating the envelope, allows the solutions for generating cupolae with base polygon which number of sides exceedes n=10, which was the maximal number of sides for cupole with the envelope consisted of twofold strip of equilateral triangles. By analyzing the elements of these polyhedra and by help of their paper models, we find geometric constructions and projection procedures by which it is possible to graphically display the cupolae. PB - Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG) C3 - PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 T1 - Forming the Cupolae With Concave Polyhedral Surfaces by Corrugating a Fourfold Strip of Equilateral Triangles EP - 374 SP - 363 UR - https://hdl.handle.net/21.15107/rcub_grafar_2047 ER -
@conference{ author = "Mišić, Slobodan and Obradović, Marija", year = "2010", abstract = "The cupolae with concave polyhedral surfaces consist of: two regular polygons, n-gone and 2n-gone in parallel planes, interconnected by an envelope constituted of series of equilateral triangles. The paper describes cupolae which originate by corrugating of a fourfold strip of equilateral triangles, forming thereby the envelope of a cupola. In this manner, a non-convex polyhedron is emerged. Such a method of corrugating the envelope, allows the solutions for generating cupolae with base polygon which number of sides exceedes n=10, which was the maximal number of sides for cupole with the envelope consisted of twofold strip of equilateral triangles. By analyzing the elements of these polyhedra and by help of their paper models, we find geometric constructions and projection procedures by which it is possible to graphically display the cupolae.", publisher = "Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)", journal = "PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010", title = "Forming the Cupolae With Concave Polyhedral Surfaces by Corrugating a Fourfold Strip of Equilateral Triangles", pages = "374-363", url = "https://hdl.handle.net/21.15107/rcub_grafar_2047" }
Mišić, S.,& Obradović, M.. (2010). Forming the Cupolae With Concave Polyhedral Surfaces by Corrugating a Fourfold Strip of Equilateral Triangles. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)., 363-374. https://hdl.handle.net/21.15107/rcub_grafar_2047
Mišić S, Obradović M. Forming the Cupolae With Concave Polyhedral Surfaces by Corrugating a Fourfold Strip of Equilateral Triangles. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010. 2010;:363-374. https://hdl.handle.net/21.15107/rcub_grafar_2047 .
Mišić, Slobodan, Obradović, Marija, "Forming the Cupolae With Concave Polyhedral Surfaces by Corrugating a Fourfold Strip of Equilateral Triangles" in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 (2010):363-374, https://hdl.handle.net/21.15107/rcub_grafar_2047 .