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.
In this tessellation, the hexagons, pentagons, and squares are all regular. The irregular polygons are equilateral decagons, as well as equilateral and concave tetrakaiicosagons.
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.
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).
This mathematical illustration of a sunflower is made of fourteen regular heptagons, fourteen irregular pentagons, and a single tetradecagon.
I made this with Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.
