October 31 – 304.

The Kuen kabuki. In mathematics, a Zoll surface, named after Otto Zoll, is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. The Kuen surface is a special case of Enneper’s negative curvature surfaces

Background: Hubble telescope. Galaxy Cluster MACS J0717, 5.4 billion light-years from Earth. It is one of the most complex galaxy clusters ever seen.



October 30 – 303.

JavaView – Exploding snubdodecahedron. The snubdodecahedron is an Archimedean solid. It has 92 faces, 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices.

Background: Hubble telescope. Infant Stars in the Small Magellanic Cloud


October 29 – 302.

JavaView – A heptahedron is a polyhedron with seven faces. All of the faces are regular, the vertices equivalent. The heptahedron is self-intersecting and therefore not considered an Archimedean solid.

Background: Hubble telescope. Jupiter red-hole close-up


October 28 – 301.

JavaView – Bottle in a sphere. The Klein bottle was first described by German mathematician Felix Klein in 1882. It is a two-dimensional, no orientable manifold. The Klein bottle has no boundary.

Background: Hubble telescope. A giant cluster of about 3,000 stars called Westerlund – for Swedish astronomer Bengt Westerlund, who discovered the grouping in the 1960s. It is located 20,000 light-years away from Earth in the constellation Carina.


October 27 – 300.

Celebrating image # 300 (65 more to go!) – from – very old (the background tiling) – to very new (the abstract shape)…

JavaView – A periodic minimal surface constructed by German mathematician Karl H. Schwarz using the following two principles:

  1. If part of the boundary of a minimal surface is a straight line, then the reflection across the line, when added to the original surface, makes another minimal surface.
  2. If a minimal surface meets a plane at right angles, then the mirror image of the plane, when added to the original surface, also makes a minimal surface.

Floor tile– same surface taken through a Lagrange spin filter.

Background: Hubble telescope. Incoming Comet ISON. Its glare can be seen at the left bottom of the foreground object.


October 26 – 299.

JavaView – “Waiting for the third sphere”. Henry Wente conjecture building up to the Wente torus – an immersed, constant mean-curvature surface with three-lobed surface. It was discovered by Dr. Henry Wente in 1984

Background: Hubble telescope. Composite Image of Galaxy Cluster 1E 0657-556


October 25 – 298.

JavaView – Cross caps. In mathematics, a cross-cap is a two-dimensional surface in  a 3D space. It is one-sided and shows a continuous image of a Möbius strip that intersects itself at interval.

Background: Hubble telescope. Dark Matter ring in Galaxy Cluster