The blue polygons are regular pentadecagons, and the yellow polygons are irregular dodecagons. There are also equilateral hexagons (orange), red squares, and black concave pentagons.

# Tag Archives: geometry

## Tessellation of Regular Dodecagons and Tetraconcave, Equilateral Octagons

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# Two Rhombic Polyhedra with Tessellated Faces

These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).

I made both of these using* Stella 4d*, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.

# Yellow Star Tessellation

In this tessellation, the hexagons, pentagons, and squares are all regular. The irregular polygons are equilateral decagons, as well as equilateral and concave tetrakaiicosagons.

# Five Variants of the Compound of Two Tetrahedra

This is the compound of two tetrahedra, also known as Johannes Kepler’s *Stella Octangula*.

I found the five variations of this polyhedral compound shown below, located deep within the stellation-series of the great rhombicuboctahedron.

These .gif images were all made using *Stella 4d*, a program you can try for free at http://www.software3d.com/Stella.php.

## Tessellation of {8, 3} Star Octagons, and Two Sizes of Squares

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# Four, Six, Nine, and Eighteen

This mathematical illustration includes two shapes of rhombi (orange and green), isosceles trapezoids (blue), regular hexagons (yellow), regular enneagons (red), and a single regular octadecagon (violet).