ARIATIONS OF CONCAVE PYRAMIDS OF SECOND SORT WITH AN EVEN NUMBER OF BASE SIDES
Keywords:
concave polyhedron, concave pyramid, deltahedral lateral surface, regular polygonal basisAbstract
Concave pyramids of second sort (CP II) are formed similarly to concave cupolae of second sort (CC II) with a comparable logic of emergence to the regular-faced convex pyramids. They are formed by enclosing the space over a regular polygonal base by the lateral deltahedral wrapper consisting of equilateral triangles meeting in common apex. The plane net is composed of double row of equilateral triangles, so it is possible to form a regular faced pyramid even with bases greater than pentagonal, whereat the obtained polyhedron will be concave. In this paper we focus on a type of concave pyramids of second sort formed over the basic polygons with an even number of sides, type CP II-B which has half the number of lateral unit cells than the type CP II-A.
Downloads
References
Emmerich D.G. (1986). Composite polyhedra
(Polyedres composites) – Topologie Strucutrale #13,
ISSN 0226-9171, Montreal, Canada.
Gabriel J.F.(1997). Beyond the cube: the architecture
of space frames and polyhedra, Wiley, 1 edition,
ISBN: 978-0-471-12261-6, New York, US.
Huybers P. (2009). Polyhedroids, An Anthology of
Structural Morphology, World scientific Publishing
Co. Pte. Ltd. pp. 49-62, ISBN: 978-981-283-720-2,
Singapore.
Huybers P. (2001). The Morphology of building
Structures, Engineering Structures 23, pp. 12-21,
ISBN: 978-3-540-43594-5, Berlin, Germany.
Johnson N.W. (1966). Convex Polyhedra with
Regular Faces, Canadian Journal of Mathematics,
University of Toronto Press, Toronto, Canada.
Mišic S., Obradovic M., Ðukanovic G. (2014).
Composite Concave Cupolae as Geometric and
Architectural Forms, Proceedings of the 16th
International Conference on Geometry and Graphics,
-8 Avgust 2014. pp. 187-198. ©Innsbruck
university press, 2014 Universität Innsbruck, 1st
edition, ISBN 978-3-902936-46-2, Innsbruck
Austria.
Obradovic M. (2012). A Group Of Polyhedra
Arised As Variations Of Concave Bicupolae Of
Second Sort, Proceedings of 3rd International
Scientific Conference MoNGeometrija 2012, Novi
Sad, jun 21-24. 2012. pp. 95-132, ISBN 978-86-
-405-7. Novi Sad, Serbia.
Obradovic M., Mišic S. (2008). Concave Regular
Faced Cupolae of Second Sort, Proceedings of 13th
ICGG, July 2008, El. Book, pp. 1-10, ISBN 978-3-
-042-6. Dresden, Germany.
Obradovic M., Mišic S., Popkonstantinovic B.,
Petrovic M., Maleševic B., Obradovic R. (2013).
Investigation of concave cupolae based polyhedral
structures and their potential application in
architecture, TTEM Journal, Vol.8., No.3, 8/9, pp
-1214, ISSN: 1840-1503, Banja Luka, Bosnia
and Hercegovina.
Obradovic M., Popkonstantinovic B., Mišic S.
(2013). On the Properties of the Concave Antiprisms
of Second Sort, FME Transactions, Vol. 41 No 3
septembar 2013. pp. 256-263, ISSN: 1451-2092,
Belgrade, Serbia.
Obradovic M. (2006). Konstruktivno – geometrijska
obrada toroidnih deltaedara sa pravilnom
poligonalnom osnovom, Doctoral disertation,
Arhitektonski fakultet Univerziteta u Beogradu,
Belgrade, Serbia.
Obradovic M., Mišic S., Popkonstantinovic B.
(2014). Concave Pyramids of Second Sort -The
Occurrence, Types, Variations, 4th International
Scientific Conference on Geometry and Graphics,
moNGeometrija 2014, jun 20-22, Preoceedings Vol
pp. 157 -168, ISBN 978-86-88601-14-6, Vlasina,
Serbia.
Downloads
Published
Issue
Section
License
Copyright (c) 2015 Journal of Industrial Design and Engineering Graphics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
