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Monthly Archives: October 2013
165Srix
In threedimensional 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 fourdimensional polytopes, known as … Continue reading
120 Undulating Dodecahedra
This is a 120cell, one of the regular polychora (fourdimensional 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
600 Undulating Tetrahedra
This is a 600cell, one of the regular polychora (fourdimensional 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
“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.
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 wellknown. 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
Polyhedron Featuring Decagons and Triangles
This was created using Stella 4d, which you may try for free at http://www.software3d.com/stella.php.