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Small Triakis Octahedron Stellations


U14Dual
U17Dual
U21Dual

R. Whorf found that there are probably several thousand stellations of the small triakis octahedron (Wenninger 1983, p. 36). In particular, the convex hulls of the great cubicuboctahedron U_(14), the Archimedean great rhombicuboctahedron A_3=U_(17), and great rhombihexahedron U_(21) are all the Archimedean truncated cube A_9, whose dual is the small triakis octahedron, so the duals of these solids (i.e., the great hexacronic icositetrahedron, great deltoidal icositetrahedron, and great rhombihexahedron) are all stellations of the small triakis octahedron (Wenninger 1983, p. 57).

SmallTriakisOctahedronStellationDiagram

The stellation diagram showing the lines of intersections of nonparallel face planes with the plane of one face are shown above (left figure). Note that the diagram appearing in Wenninger (1989, p. 38, Fig. 28) corresponds to just the central "star" portion (right figure).


See also

Archimedean Dual Stellations, Fully Supported Stellation, Miller's Rules, Small Triakis Octahedron, Stellation

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References

Webb, R. "Enumeration of Stellations." http://www.software3d.com/Enumerate.php.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, pp. 36, 38, and 57-58, 1983.

Referenced on Wolfram|Alpha

Small Triakis Octahedron Stellations

Cite this as:

Weisstein, Eric W. "Small Triakis Octahedron Stellations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmallTriakisOctahedronStellations.html

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