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Constructing the Stewart G3 from a Triangular Hebesphenorotunda

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The Stewart G3 is a concave polyhedron made from seven triangles, three squares and three pentagons.

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This Demonstration shows a construction of the Stewart G3 from a triangular hebesphenorotunda. We begin with a nonconvex solid consisting of five parts: the red triangular hebesphenorotunda, three brown congruent solids and a blue triangular pyramid. At the end, the four parts are a dissection of Stewart G3.

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Contributed by: Izidor Hafner (January 2024)
Open content licensed under CC BY-NC-SA

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In [1] we observed that the triangular hebesphenorotunda and the Steward toroid G3 can be derived from golden rhombic solids. We also made paper models and found that these solids could be dissected into a golden rhombic solid. We made a Zometool model of such a solid.

Reference

[1] I. Hafner, "Dissection of Triangular Hebesphenorotunda, Steward Toroid, and Drilled Pentagonal Gyrobicupola," VisMath, 9(2), 2007. https://www.mi.sanu.ac.rs/vismath/hafnervisual/visual43A/Visual43A.html.

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