Changing Hexecontahedron

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The rhombic hexecontahedron consists of 20 acute golden rhombohedra. Its symmetry group is icosahedral, so there are 15 axes of 2-fold rotational symmetry. Two points where an axis of -fold rotational symmetry punctures the surface of a polyhedron are called -poles. So the hexecontahedron has 30 2-poles, which are shown in the controls. Choosing from them using the numbered buttons, you can replace two acute rhombohedra that are adjacent to a 2-pole by two obtuse rhombohedra, or alternatively, you can augment the polyhedron by two obtuse rhombohedra. When you click a number, the buttons that correspond to adjacent 2-poles disappear, because these poles are no longer in play. This Demonstration also shows four prepared examples.

Contributed by: Izidor Hafner (August 2014)
Open content licensed under CC BY-NC-SA




[1] P. R. Cromwell, Polyhedra, Cambridge: Cambridge University Press, 1997.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.