Tag Archives: pentagon

A Pentagonal Mandala In Primary Colors

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A Pentagonal Mandala In Primary Colors

Polyhedron Featuring Regular Pentagons, Isosceles Triangles, and Overlapping Regular Enneagons

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Polyhedron Featuring Regular Pentagons, Isosceles Triangles, and Overlapping Regular Enneagons

This is similar to the polyhedron seen here: https://robertlovespi.wordpress.com/2014/05/21/polyhedron-featuring-twenty-regular-nonagons-twelve-regular-pentagons-and-sixty-isosceles-triangles/. The difference is that the enneagons (also called nonagons) are closer to this polyhedron’s center, causing them to overlap slightly.

Software credit: visit http://www.software3d.com/Stella.php for a free trial download of Stella 4d, the program I used to create this image.

 

Polyhedron Featuring Twenty Regular Enneagons, Twelve Regular Pentagons, and Sixty Isosceles Triangles

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Polyhedron Featuring Twenty Regular Nonagons, Twelve Regular Pentagons, and Sixty Isosceles Triangles

If the isosceles triangles in this polyhedron were close enough to being equilateral that close inspection would be required to tell the difference, this would be a near-miss to the Johnson Solids. However, in my opinion, this doesn’t meet that test — so I’m calling this a “near-near-miss,” instead.

Software credit: visit this website if you would like to try a free trial download of Stella 4d, the program I used to create this image.

140-Faced Polyhedron Featuring Twenty Nonagons, Plus Sixty Each of Two Types of Pentagon

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140-Faced Polyhedron Featuring Twenty Nonagons, Plus Sixty Each of Two Types of Pentagon

Software credit: just visit http://www.software3d.com/Stella.php to try or buy the software, Stella 4d, which I used to make this polyhedron.

Pentagonal Mandala III

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Pentagonal Mandala III

I suspect that this could be continued outward indefinitely, as a radial and aperiodic tessellation, using only the four polygons you see, repeatedly, here. However, I have no proof of this.

Pentagonal Mandala II

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Pentagonal Mandala II

A Polyhedron with 122 Faces

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A Polyhedron with 122 Faces

The 122 faces are twenty blue, irregular hexagons; thirty red, irregular hexagons; 60 rectangles, and twelve regular pentagons.

Software credit: just visit http://www.software3d.com.Stella.php, and look for the free trial download of Stella 4d, the program I used to make this rotating image.

Dodecahedron Made of Rhombic Triacontahedra

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Dodecahedron Made of Rhombic Triacontahedra

In the last post, I showed that five rhombic triacontahedra can be stuck together to form a pentagonal ring. The next logical step is shown here: using such pentagonal rings to construct an entire dodecahedron made of rhombic triacontahedra.

Software credit: see http://www.software3d.com/stella.php.

Pentagonal Ring of Rhombic Triacontahedra

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Pentagonal Ring of Rhombic Triacontahedra

Software credit: http://www.software3d.com/Stella.php.

Decorated Snub Cube

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Decorated Snub Cube

Geometer’s Sketchpad and MS-Paint were used to make the “Metapentagon” design shown in the last post. After that, I used Stella 4d (see http://www.software3d.com/stella.php) to project this image onto each face of a snub cube, and create this rotating .gif file.