Gyroelongated bipyramid

Special members in the family of gyroelongated bipyramids

The gyroelongated bipyramids are the polyhedra constructed with a bipyramid and an antiprism. The bipyramid is sliced into two congruent pyramids and then attached to the bases of an antiprism in between; such a process of construction is known as gyroelongation. The resulting construction has triangular faces, classified as simplicial polyhedron. There are infinitely many members of gyroelongated bipyramids.[1]

Some members are special cases for having equilateral triangular faces, which are known as deltahedra: the gyroelongated square bipyramid[2] and regular icosahedron.[3][4] For a gyroelongated triangular bipyramid, it is a non-convex deltahedron because its faces are coplanar, thereby it is not strictly convex. Considering that each pair of its triangles merged into rhombi, the resulting polyhedron can be seen as a trigonal trapezohedron.

References

  1. ^ Kumar, C. P. Anil (2020). "On the Coherent Labelling Conjecture of a Polyhedron in Three Dimensions". arXiv:1801.08685 [math.CO].
  2. ^ Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.
  3. ^ Gailiunas, Paul (2023). "Kagome from Deltahedra". In Holdener, Judy; Torrence, Eve; Fong, Chamberlain; Seaton, Katherine; Kaplan, Craig S. (eds.). Bridges Conference Proceedings. Phoenix, Arizona: Tessellations Publishing. pp. 337–344. See p. 339.
  4. ^ Trigg, Charles W. (1978). "An Infinite Class of Deltahedra". Mathematics Magazine. 51 (1): 55–57. doi:10.2307/2689647. JSTOR 2689647.
This article is issued from Wikipedia. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.