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.
This is the icosidodecahedron. It’s one of the thirteen Archimedean solids. To make an expanded version of it, I first augmented each of its faces with a prism.
Next, I formed the augmented icosidodecahedron’s convex hull.
This expanded icosidodecahedron has the twelve pentagonal faces (shown in red) and twenty triangular faces (shown in blue) of the original icosidodechedron. It also has sixty rectangular faces (yellow), and sixty isosceles triangles (shown in green). That’s a total of 152 faces.
To do all of this, I used a program called Stella 4d. If you’d like to try Stella for yourself, for free, just visit this website: http://www.software3d.com/Stella.php.
In this tessellation, golden rectangles are shown in yellow. The orange darts are each made of two golden gnomons, joined at a leg — while the blue rhombi are each made of two golden triangles, sharing a base.
To make this rotating .gif, I navigated to the rhombic triacontahedron in Stella 4d, and then loaded images onto its thirty faces, with the image being the one I blogged in the post right before this one. This program, Stella, has a free trial download you can get right here.
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