# Discrete S-Conical Scherk Tower

Alexander I. Bobenko, Tim Hoffmann, Benno König, Stefan Sechelmann

### Description

The classical Scherk surfaces were discovered by H.F. Scherk in [1]. For a comprehensive treatment of the Scherk minimal Surfaces see: [2]. We present a discrete version of the singly periodic Scherk surface, also known as Scherk's second minimal surface. It is a discrete s-conical version, see [3], of this surface, see [A Fundamental Piece] and the corresponding Gauss image [Discrete Gauss Map]. It is constructed using orthogonal circle patterns on the sphere (see [4]) to create a discrete version of the Gauss image.

In additional to this, we present data for the the discrete associate family. Scherk's discrete singly periodic minimal surface contains Scherk's doubly periodic surface at $\gamma=\frac{\pi}{2}$ in the associate family, see [Conjugate Scherk Minimal Surface]. This surface is parameterized along asymptotic lines as in the smooth case.

Other digital versions of this model can be found at [5], and [6], and [7].

### References

#### Prof. Dr. Alexander I. Bobenko   +

Projects: A01, A02, C01, B02, Z, CaP, II
University: TU Berlin, Institut für Mathematik, MA 881
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31424655
E-Mail: bobenko[at]math.tu-berlin.de
Website: http://page.math.tu-berlin.de/~bobenko/

#### Prof. Dr. Tim Hoffmann   +

Projects: A02
University: TU München
E-Mail: hoffmant[at]ma.tum.de
Website: http://www-m10.ma.tum.de/bin/view/Lehrstuhl/TimHoffmann

#### Benno König   +

Projects: A02
University: TU München

#### Dr. Stefan Sechelmann   +

Projects: A01
University: TU Berlin
E-Mail: sechel[at]math.tu-berlin.de