I was preparing some artwork (The 12-30 project, #211 – July 30 ) for an upcoming exhibit and I clicked the emboss filter – almost by accident. And here it popped up – a next to perfect representation of a (topological) 4D perspective of a Klein bottle – from the outside looking in. Thanks @Mathematica, and thanks #Richard Bennigan for the original script.

# mathematics

# Jan 6,2016

The 12-30 project will continue with a life of its own this time. I’ll keep posting images as they come – when they are included in real-time exhibitions. The original (large files) will be printed 18×18 or 24×24 on aluminum or linen canvas depending on the venue and the image.

This one (#150 in the project) is part of an exhibit of my work at the JMM conference in Seattle, Jan 6-9.

# 278

October 5 – 278

JavaView – Distant geometries.The rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid. The Rhombic Triacontahedron describes the nesting of the five Platonic Solids: icosahedron, dodecahedron, cube, tetrahedron, octahedron. It shows that the 5 nested Platonic Solids may not only grow and contract to infinity, but do so in a perfectly harmonious way.

Bottom left, 2 small garnets. Background: Hubble telescope – The heart of Starburst Galaxy M82

# 276

October 3 – 276

JavaView. Icosahedron. The icosahedron. is a 20-face polyhedron. There are 43,380 distinct nets for the icosahedron. Fifteen golden rectangles span the interior of the icosahedron. These rectangles have 30 edges, and each edge pairs up with its opposite edge to form a golden rectangle. Two icosahedra appear as polyhedral “stars” in M. C. Escher’s 1948 wood engraving “Stars”.

Background – Hubble view of the sunward plunging comet ISON. It was discovered in 2012 by Vitali Nevski and Artyom Novichonok and named after the Russia-based International Scientific Optical Network

# 232

August 20 – 232.

Escherlike. Pentagon tiling to celebrate Casey Mann, Jennifer McLoud and David Von Derau of the University of Washington Bothell who discovered a fifteenth pentagon fitting seamlessly on a flat surface and the first new one to be found in 30 years.

Geraud Bousquet, author of Escher-Like is working at integrating this new shape in the program’s library.