**Ein Vierteljahrhundert Mathematik**(25 Years Mathematics) (2003)

Spektrum der Wissenschaft

The *Boy surface* is an immersion of the projective plane, a
non-orientable surface. The image enhances the structure of the
self-intersection of the surface including the single triple point.
The image is used as cover image of an
article by Ian Stewart in
Spektrum der Wissenschaft.

**Digest Wissenschaftliches Rechnen**(Scientific Computing) (1999)

Spektrum der Wissenschaft

In hyperbolic space exist four regular platonic solids whose
vertices lie in infinity. In the image *Hyperbolic Polyhedra*
(K. Polthier, 1999) the solids are visualized in the Poincare
representation where the infinite boundary of hyperbolic space is
the unit sphere. Further details are available in the following
article.

**Video Touching Soap Films**(1999)

Springer VideoMATH

English edition of video *Touching Soap Films* (A. Arnez, K.
Polthier, M. Steffens, C. Teitzel) appeared in the new series of
mathematical videos of Springer. Cover shows sample scenes from
Touching Soap Films.

**Experimental Mathematics**(1997) vol 1 (6)

The *Tetra Surface* is a compact surface with constant mean
curvature (K. Große-Brauckmann and K. Polthier, 1997), and has the
symmetry of a regular tetrahedron. It belongs to a rare set of new
compact CMC surfaces found by numerical experiments. For details,
see the corresponding article Compact
Constant Mean Curvature Surfaces With Low Genus

**Moderne Mathematik**by Gerd Faltings (1996)

Spektrum der Wissenschaft

The *Hyperbolic Minimal Surface* (K. Polthier, 1993) is a
triply periodic minimal surface in hyperbolic three-space. It
belongs to a family of surfaces whose fundamental domains are given
as solution of free-boundary value problems in hyperbolic
orthoschemes. Details are available in the following
paper.

**Elliptic and Parabolic Methods in Geometry**(1996)

by Ben Chow, Robert Gulliver, Silvio Levy and John Sullivan, AK Peters Publisher

The *Penta Surface* (K. Große-Brauckmann and K. Polthier,
1996) is a new compact constant mean curvature surface with genus
five and very few bubbles. Compact CMC surfaces have a long history
in geometry, more details are given in
Numerical Examples of Compact Constant Mean Curvature Surfaces.

**Sources of Hyperbolic Geometry**(1996)

by John Stillwell, AMS Publisher

*Hyperbolic Spaces* (K. Polthier, 1995) can be represented
by a number of different models. The picture relates the hyperboloid
model and the Poincaré model, both being regularly tessellated by a
2-3-7 triangle. The picture is part of an animation of hyperbolic
space shown in the video Touching Soap
Films.

**Mathematical Intelligencer**(Spring 1995)

Springer Verlag

There are exactly four *Ideal Hyperbolic Polyhedra* (K.
Polthier, 1995), i.e. platonic solids in hyperbolic space whose
vertices are at the sphere at infinity. The picture was created for
an article of Ruth Kellerhals on the volume of hyperbolic polyhedra.

**Video Palast der Seifenhäute**(1995)

Komplett Video

The *Kaleidoskop* is a still picture by A. Arnez, K.
Polthier, C. Teitzel and M. Steffens (1995) from an animation in the
video Palast der Seifenhäute where
Kalle enters hyperbolic space. The animation uses a specific
arrangement of reflectors to obtain the kaleidoscopic effect.

**Video Palast der Seifenhäute**(1995)

Bild der Wissenschaft

The cover of the german edition of the video
Touching Soap Films shows the *
Bidenoid *minimal surface discovered by H. Karcher. It's
existence manifests the enormous possibilities in modifying existing
minimal surfaces by including further catenoid ends. A animation of
this process is shown in detail in the video. Cover picture by A.
Arnez, K. Polthier, C. Teitzel and M. Steffens, 1995.

**Calendar Digital Dance**(1992)

Saitzek Verlag

The calendar *Digital Dance 1992* with cover image *
Cochlea* (K. Polthier, 1991) was published by R. Saitzek Verlag,
Bremen, with contributions of five authors. Together with Martin
Rumpf I contributed a number of images we had made using the
software GRAPE. See
the calendar section for
further images and the article section
for more information on hyperbolic minimal surfaces like the shown
hyperbolic helicoid.