This is a modification of the well-known tessellation of the plane with squares and regular octagons.
Octagonal Spirals
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A Tessellation of Regular Decagons and Bowtie Hexagons
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A Tessellation of Concave, Equilateral Pentagons, Together with Tetraconcave, Equilateral Octagons
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Tessellation Featuring Circles and Rhombi
Is there anything more relaxing than constructing a tessellation?
A Concave Polyhedron Featuring Eight Regular Dodecagons
This 110-faced polyhedron has, in addition to the eight regular dodecagons, six rectangles, and 96 triangles. I made it using Stella 4d, a program you can try for free, as a demo version, at http://www.software3d.com/Stella.php. I wish I could remember how I made it!
Fortunately, I have many friends who are more knowledgeable than I, when it comes to mathematics. Perhaps one of them will be able to solve this mystery.
Urgent! Hyundai Safety Recall
This is real, and our car is one of the ones being recalled. We have a phone call in to the nearest Hyundai dealership, and are waiting for a phone call with instructions from them. They’ll fix this potentially dangerous problem involving brake lights for free. All you need to do is adjust the Google search terms to match your Hyundai car, and then add information about your location, so that the search engine can return the specifics you need to find the Hyundai dealership nearest you, in order to keep your family safe.
Attention, Teachers of Arkansas!
This is a dangerous time to be a teacher. Each of us needs an organization that looks out for us — and, here in Arkansas, we have one. It’s the AEA (Arkansas Education Association). I’ve been a member for years, and can’t imagine going back to school without my AEA membership, and the protection it offers. The easiest way to join is at this page: https://www.aeaonline.org/join/.
The “Dungeons & Dragons” Alignment System, Applied to Characters From the Pages of “Daredevil” Comic Books
This nine-part alignment system comes from Dungeons and Dragons, and these images come from various Marvel comics (although I found them with Wikipedia and Google-searches). All I did was place these nine characters into the nine D&D alignment categories — which was the fun part of making this chart.
A Symmetrohedron Featuring Regular Heptagons, Regular Hexagons, Irregular Hexagons, and Irregular Pentagon-Pairs
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 twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.
A Symmetrohedron Featuring Regular Heptagons and Hexagons, Along with Irregular Quadrilaterals and Triangles
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.
