This is an adjustment and extension of the radial tessellation shown in the most recent post here. I am now confident that this pattern could be extended outward, without limit.
I believe this can be continued, outward, indefinitely. I also believe it is aperiodic. However, I do not have a proof for either of these conjectures.
The yellow triangles are golden gnomons, while the blue triangles have angles of 108, ~26.3, and ~45.7 degrees.
This began with an {8/3} star octagon. It then started spreading.
The stars on the pentagonal faces were drawn using Geometer’s Sketchpad and MS-Paint. The icosidodecahedron itself was created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
Polyhedral excavation is the opposite of augmentation. In this excavated tetrahedron, short pyramids have been removed from each face. I made this using Stella 4d, which can be tried for free at this website.
RobertLovesPi.net 