TOPICS
Search

Archimedean Solid Stellations

The Archimedean solids in general have many stellations. Examples of Archimedean solid stellations include the dodecadodecahedron and great icosidodecahedron.

The following table extracted from Webb gives a partial enumeration. In the table, E denotes counts of enantiomorphous stellations and C counts of chiral stellations.

cell typescell typesfully supportedfully supportedMiller's rulesMiller's rules
solidECECEC
cuboctahedron80130210
great rhombicosidodecahedron130164226575482
great rhombicuboctahedron3217325419378
icosidodecahedron3294324157071672
small rhombicosidodecahedron124149133925171298698112224
small rhombicuboctahedron3117333915488
snub cube027418299050957758
snub dodecahedron01940579
truncated cube90180450
truncated dodecahedron3510600541128761995
truncated icosahedron3510579538162782259
truncated octahedron90180450
truncated tetrahedron4060100

There are also many Archimedean dual stellations.

See also

Archimedean Dual Stellations, Archimedean Solid, Catalan Solid, Fully Supported Stellation, Icosidodecahedron Stellations, Miller's Rules, Stellation

Explore with Wolfram|Alpha

References

Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform Polyhedra." Phil. Trans. Roy. Soc. London Ser. A 246, 401-450, 1954.Webb, R. "Enumeration of Stellations." http://www.software3d.com/Enumerate.php.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, 1991.Wenninger, M. J. "Commentary on the Stellation of the Archimedean Solids." In Polyhedron Models. New York: Cambridge University Press, pp. 66-72, 1989.

Referenced on Wolfram|Alpha

Archimedean Solid Stellations

Cite this as:

Weisstein, Eric W. "Archimedean Solid Stellations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArchimedeanSolidStellations.html

Subject classifications