Construction of Polyhedra Whose Vertices are Points on Curve Which Lying on Lemniscatic Torus with Mathematica

Ricardo Velezmoro-León, Robert Ipanaqué-Chero, Marcela Velásquez V. Fernández, Jorge Jimenez Gomez

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Polyhedra are widely used in art, science and technology. Faced with this situation, the following research question is formulated: Can new polyhedral structures be generated from another mathematical object such as a lemniscatic torus? For this question, the results we obtained are two particular cases whose vertices are points that belong to curves that lie on a lemniscatic torus: the first, a new polyhedron that has regular trapezoids in the equatorial zone, and the second, one that has triangles equal to each other. For both polyhedra, there exists an antipodal symmetry in the Arctic and Antarctic zones. Emphasis is placed on the construction of two convex polyhedra above mentioned: a one with 18-faces and other with 36-faces, using the scientific software Mathematica v.11.2. We also determine their total areas which respectively approximate 9.51 R2 and 10.44 R2. Likewise, the volume of each one is approximately 2.41 R3 and 4.19 R3, respectively. Moreover, they being inscribed in a sphere of radius R, and their opposite faces are not parallel.

Original languageEnglish
Title of host publicationComputational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings
EditorsOsvaldo Gervasi, Beniamino Murgante, Sanjay Misra, Chiara Garau, Ivan Blecic, David Taniar, Bernady O. Apduhan, Ana Maria Rocha, Eufemia Tarantino, Carmelo Maria Torre
PublisherSpringer Science and Business Media Deutschland GmbH
Pages3-17
Number of pages15
ISBN (Print)9783030869595
DOIs
StatePublished - 2021
Event21st International Conference on Computational Science and Its Applications, ICCSA 2021 - Virtual, Online
Duration: 13 Sep 202116 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12950 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Conference on Computational Science and Its Applications, ICCSA 2021
CityVirtual, Online
Period13/09/2116/09/21

Keywords

  • Lemniscatic torus
  • Polyhedral
  • Wolfram mathematica

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