Monthly Archives: October 2013

165-Srix

In three-dimensional space, there are five Platonic and thirteen Archimedean polyhedra, plus numerous other shapes, in several categories. The whole collection can appear to be quite a confusing jumble — until, and unless, you start surveying four-dimensional polytopes, known as … Continue reading

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120 Undulating Dodecahedra

This is a 120-cell, one of the regular polychora (four-dimensional polytopes), with its edges and vertices rendered invisible, and its dodecahedral cells shrunk somewhat, to put some empty space between them. It’s rotating in hyperspace, and what you are seeing … Continue reading

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600 Undulating Tetrahedra

This is a 600-cell, one of the regular polychora (four-dimensional polytopes), with its edges and vertices rendered invisible, and its cells shrunk so that they do not touch. It’s rotating in hyperspace, and what you are seeing at any given … Continue reading

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A Ball of Kites

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“All Is Number”

“All is number” was a motto of the ancient Pythagorean Society. I thought it would also make a good title for this geometrical design.

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When Must the Four Perpendicular Bisectors of the Sides of a Quadrilateral Be Concurrent?

The perpendicular bisectors of the three sides of any triangle must be concurrent, as is well-known. However, this is not true of quadrilaterals. For quadrilaterals, the four perpendicular bisectors may be concurrent, or not. So when must they be? The … Continue reading

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Polyhedron Featuring Decagons and Triangles

This was created using Stella 4d, which you may try for free at http://www.software3d.com/stella.php.

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