## A Quintic with 15 Cusps

The quintic with 15 cusps is a so-called world record surface: To our knowledge, it is not known if there may be a quintic with more than 15 cusps although it is known that a quintic cannot have more than 20 cusps.

The quintic with 15 cusps is a so-called world record surface: To our knowledge, it is not known if there may be a quintic with more than 15 cusps although it is known that a quintic cannot have more than 20 cusps.

The gyroid is a modern classic. It is a so-called minimal surface. Our object is an approximation of it in terms of sine and cosine. This one shows more tunnels than our other version.

The sculpture we present here is a 3D-printed modern object consisting of the 27 lines only, and a thin part of the surface as a border.

The gyroid is a modern classic. It is a so-called minimal surface. Our object is an approximation of it in terms of sine and cosine.

The complete series of 45 types of cubic surfaces with only finitely many singularities and lines. We provide links to put a complete set of several cubic surface models into your shopping cart.

The Barth Sextic is probably the most famous example of the sometimes so-called world record surfaces. This post shows a smoothed variant of it.

This version of Clebsch's famous diagonal surface model features colored lines. One intersects the surfaces in a line and a hyperbola, the another one in three lines.

A Togliatti quintic surface is a so-called world record surface. Among all quintic surfaces, it has the maximum possible number of singularities, namely 31. Our model is a smoothed version of such a surface.

This object looks like a piece of art. But in fact, it is "just" a mathematical curve, called 7/3 torus knot. Imagine a donut, and then tie a cord around it in some interesting way.

Our modern version of Klein's historical cubic surface model with four singularities is the main figure in our photo from the series "math sculptures in context". It is the pure white version with its 9 straight lines.