Tag Archives: symmetrohedra

Four Symmetrohedra

Symmetrohedra are polyhedra with some form of polyhedral symmetry, all faces convex, and many (but not all) faces regular. Here are four I have found using Stella 4d, a polyhedron-manipulation program you can try for yourself at http://www.software3d.com/Stella.php. The second … Continue reading

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Bowtie Cubes in a Polyhedral Honeycomb

This polyhedron has been described here as a “bowtie cube.” It is possible to augment its six dodecagonal faces with additional bowtie cubes. Also, the bowtie cube’s hexagonal faces may be augmented by truncated octahedra. These two polyhedra “tessellate” space, together … Continue reading

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A Symmetrohedron with 74 Faces

Symmetrohedra have many regular faces, but irregular faces are allowed in them as well. The octagons, hexagons, and squares in this polyhedron are regular, but the 48 triangles are scalene. Here’s what it looks like with these triangles rendered invisible: … Continue reading

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The Second of Dave Smith’s “Bowtie” Polyhedral Discoveries, and Related Polyhedra

Dave Smith discovered the polyhedron in the last post here, shown below, with the faces hidden, to reveal how the edges appear on the back side of the figure, as it rotates. (Other views of it may be found here.) … Continue reading

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Two Polyhedra Featuring Twenty Regular Octadecagons Each

The first of these two polyhedra also includes isosceles triangles, two types of isosceles trapezoids, and twelve regular pentagons. It is also possible to make a similar polyhedron where the twelve pentagons are replaced by regular decagons, but only by … Continue reading

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A Symmetrohedron Featuring Regular Dodecagons, Regular Octagons, Isosceles Trapezoids, and Narrow Rectangles

I made this using Stella 4d, software available at http://www.software3d.com/Stella.php.

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Two Symmetrohedra Featuring Regular Pentadecagons

I’ve posted “bowtie” symmetrohedra on this blog, before, which I thought I had discovered before anyone else — only to find, later, that other researchers had found the exact same polyhedra first. Those posts have now been edited to include … Continue reading

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