TY - GEN
T1 - Construction of Polyhedra Whose Vertices are Points on Curve Which Lying on Lemniscatic Torus with Mathematica
AU - Velezmoro-León, Ricardo
AU - Ipanaqué-Chero, Robert
AU - Fernández, Marcela Velásquez V.
AU - Gomez, Jorge Jimenez
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Lemniscatic torus
KW - Polyhedral
KW - Wolfram mathematica
UR - http://www.scopus.com/inward/record.url?scp=85125271484&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-86960-1_1
DO - 10.1007/978-3-030-86960-1_1
M3 - Conference contribution
AN - SCOPUS:85125271484
SN - 9783030869595
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 3
EP - 17
BT - Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings
A2 - Gervasi, Osvaldo
A2 - Murgante, Beniamino
A2 - Misra, Sanjay
A2 - Garau, Chiara
A2 - Blecic, Ivan
A2 - Taniar, David
A2 - Apduhan, Bernady O.
A2 - Rocha, Ana Maria
A2 - Tarantino, Eufemia
A2 - Torre, Carmelo Maria
PB - Springer Science and Business Media Deutschland GmbH
T2 - 21st International Conference on Computational Science and Its Applications, ICCSA 2021
Y2 - 13 September 2021 through 16 September 2021
ER -