vier mal drei (2012)
Hagen Hilderhof

by Franco Laeri

The sculpture by Hagen Hilderhof “Four times Three” (2012) in the courtyard of the Physics Learning Center. Size: 137cm x 153 cm. Photo: F. Laeri

The artist Hagen Hilderhof

1937 born in Heidelberg, grew up in Wertheim am Main
1955 – 1958 Traineeship with architects in Würzburg and Düsseldorf
ab 1959 Freelance sculptor in Düsseldorf
1981 – 1992 Lectureship for the subject “Design Theory” at the Gesamthochschule-University Wuppertal
today Hagen Hilderhof lives and works in Michelstadt and Düsseldorf

See also the Wikipedia entry at

Hagen Hilderhof's sculptures have been shown in exhibitions in Germany, Australia, Netherlands, France, Poland, Russia, Switzerland, Great Britain and China.

Sculptures by Hagen Hilderhof are in public space in Amorbach, Darmstadt, Düsseldorf, Essen, Heilbronn, Skulpturenmuseum Marl, Michelstadt, Mühlheim/Ruhr, Neckarsulm.

His way of working

Hagen Hilderhof characterizes his working method in the following way:

“My work with sculpture began in 1959 with investigations into the interchangeability of two angle strips with legs of unequal length (permutations of L and L'), taking into account their assignment in space. From this and from related derivations – such as from double triangles – complex structures developed, spiral rows, constructions spreading out two-dimensionally or spatially.

By virtue of their own regularity, cells of four, six, eight or more units organized themselves, and their ability to communicate with neighboring cells (identical or mirror-image) was investigated and utilized” [1].

I base my work on the aesthetics of mathematically calculable forms as an objectified form of expression. My endeavor is to find a self-organizing structure that I help determine by adding and cropping. [2, 3]

Hagen Hilderhof has pursued this program with great consistency and developed it further and further. He is considered one of the most important constructivist sculptors in Germany today.

For several years, Hagen Hilderhof has been concerned with bodies consisting of rhomboids [4] and joined into rhombohedrons [5, 6], which are then in turn grouped and arranged into a sculpture. He develops his sculptures largely in cardboard, which are then realized in Corten steel, aluminum or bronze, often on a larger scale.

Reference of the sculpture to the place

Obtuse rhombohedron, 109.47

The sculpture is located in the Learning Center of the Physics Department. In the study of physics, solid state physics is an important subject area in which remarkable research results have been achieved in the last 20 years. During this time, 7 Nobel Prizes have been awarded for new discoveries in the field of solid state physics, with one laureate, Peter Grünberg (2007), being a Darmstadt alumnus.

A central theme of the solid body is its internal structure, the ordering principle of which is spatial symmetries, which is particularly vividly seen in the form of “crystals”. One of the important crystal structures is the one with a cubic crystal lattice.

Crystal lattices are characterized by their unit cell. The unit cell carries all the symmetry elements of the lattice structure in question. By repeating the appropriate symmetry operations on the unit cell, the whole three-dimensional space is filled without gaps. An important member of the cubic lattice family is the cubic space-centered lattice (about 30% of the elements; such as K, Rb, Cs, V, Nb, Ta, Cr, Mo or W). Its primitive unit cell is an obtuse-angled rhombohedron whose edges make an angle of 109.471 degrees.

The rhombohedra which form the basic bodies in Hilderhof's sculpture are exactly such rhombohedra. Hilderhof thus works with rhombohedra which correspond to the primitive unit cell of the cubic space-centered crystal lattice. If these rhombohedra were joined together in a nice regular way, a compact body would result.

Now, instead of regularly inserting one rhombohedron next to the other, Hilderhof “forgets” to insert one every now and then. This would create gaps in the space – missing parts. But Hilderhof continues to design. Instead of adding rhombohedron to rhombohedron, he also twists them slightly against each other. In this way, further “crystal construction errors” are created – just as occurs in nature when the growth conditions of a crystal are disturbed by the environment.

As you can try out for yourself with a cardboard model, the same basic polyhedron (opens in new tab) , i.e. the above rhombus, can also be assembled into an acute-angled rhombohedron (opens in new tab) in which the edges make an angle of 70.529 degrees. In the present sculpture, Hilderhof has used four identical units, each consisting of 2 acute-angled and one obtuse-angled double rhombohedron. He then joined these together with mentioned disturbances (hence the title of the sculpture “Four times Three”).

Look at the sculpture: do you recognize the principle of construction?

[1] Krimmel, Bernd [Hrsg.] Exhibition catalogSymmetrie in Kunst,
Natur und Wissenschaft – Mathildenhöhe Darmstadt 1.Juni bis 24 August 1986
, Volume 2 : Kunst, Darmstadt 1986
[2] Hilderhof, Hagen Skulpturen, Michelstadt 2007, Page 8.
[3] Lepsien Art Foundation [Hrsg.] Hagen Hilderhof Skulpturen–Skulptures, Artevie
Publishing, Berlin 2016, Page 95
[4] Udo Hebisch, Rhombenkörper
[5] B. Grünbaum 2010
[6] Bilinski, Stanko Über die Ordnungszahl der Klassen Eulerscher Polyeder, Arch. Math.
(Springer) 10, 180-186 1959;