Tag Archives: trapezoid

A Chiral Polyhedron Made of Kites and Triangles, Along with Its Dual, Made of Triangles and Isosceles Trapezoids

To make this polyhedron using Stella 4d (available here), one starts with the icosahedron, drops the symmetry of the model down from icosahedral to tetrahedral, and then stellates it once. The result is a chiral solid featuring four triangular faces … 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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The Beginning of an Attempt to Create an Aperiodic Tessellation of Golden Trapezoids

I’m not sure where this is going next. It uses the trapezoids described at the end of the last post. It’s unfinished . . . but if I leave it here, I know I’ll be able to find it later.

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A Polyhedral Demonstration of the Fact That Twenty Times Four Is Eighty

The Platonic solid known as the icosahedron has twenty triangular faces. This polyhedron resembles the icosahedron, but with each of the icosahedron’s triangles replaced by a panel of four faces:  three isosceles trapezoids surrounding a central triangle. Since (20)(4) = … Continue reading

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This Space Station for Geometricians Has, as Outer Hulls, Twelve Trapezoids, and Six Parallelograms with One Square Window / Docking Port Each

I can’t think of any good reasons for geometricans not to have their own space station, and I know what we’d do there:  we’d work on geometry (also known informally as “playing with shapes”). My suggestion for this space station’s … Continue reading

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Dodecahedral Polyhedron Featuring Regular Icosagons, Regular Hexagons, Rectangles, and Isosceles Trapezoids

Created with software you can try and/or buy at http://www.software3d.com.Stella.php.

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Cube-Based Polyhedron Featuring Regular Icosagons, Equilateral Triangles, Isosceles Trapezoids, and Rectangles

Created with software you can try and/or buy at http://www.software3d.com.Stella.php.

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