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. 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.
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