A Symmetrohedron Featuring Regular Heptagons and Hexagons, Along with Irregular Quadrilaterals and Triangles

Posted on 1 August 2020 by RobertLovesPi

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

This particular symmetrohedron features 12 faces which are regular heptagons, and 8 faces which are regular hexagons. The irregular faces are 12 isosceles triangles, 24 isosceles trapezoids, and 6 rectangles, for a total of 62 faces. It has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

Tessellation Involving Hexagons, Pentagons, and Other Polygons

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pentagons and hexagons

Trump’s Impeachment Troubles Started One Year Ago Today

Posted on 25 July 2020 by RobertLovesPi

July 25

One year ago: the infamous July 25th phone call. That led to Trump’s impeachment, but few think of it now because we’re neck-deep in the COVID-19 pandemic. Impeachment occurred before the masked age began. He didn’t get removed by the Senate, but he’s quite likely to get removed by voters in the November election. He may not leave the White House voluntarily, which would create a shameful spectacle, but he’ll be escorted away come Inauguration Day — even if they have to literally drag him off, kicking and screaming.

A Faceted Truncated Octahedron with Twenty Faces

Posted on 25 July 2020 by RobertLovesPi

Faceted Trunc Octa

The twenty faces of this polyhedron are six small blue squares, six interpenetrating, larger red squares, and eight irregular, interpenetrating yellow hexagons. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php. The squares are easy to find, but it can be a challenge to see the yellow hexagons. In the .gif below, all of the yellow faces but one are hidden, which should make it easier to see where the hexagons are positioned, relative to the squares.