Page 49 - Studio International - December 1970

The hepta-seven, hedron-side is initially con- light reflection observed. See 'Three Axis
structed of eight triangular sides like the Holding Four Rings'; the Steiner Surface
octahedron and an inside structure of three having four equal sides like the 'Tetrahedron'.
squares perpendicularly intersecting at the My math. adviser, Dr Erna Herrey, Pro-
diagonals. These lines of intersection are also fessor of Physics, member of the Doctoral
the three axes; height, width and depth. Of Faculty of the City University of New York,
the eight triangles, alternating four have been has devised a structure of ovals from the for-
cut away; thus four triangles and three mula of the Steiner Surface:
squares create the `Heptahedron'. y^2 z^2 + z^2 x^2 + x^2 y^2 + zyx = 0
The strange characteristic of this form is that See 'Intersecting Ovals', transparent multi-
in its centre point and along the axis it comes coloured and white opaque and the structure
to nothing, but the thickness of a material. of all shown Steiner Surfaces.
This characteristic of the Heptahedron' is The Steiner Surface is one of approximately
shared with the 'Steiner Surface'. one hundred mathematical models at Colum-
`Just as the simple polyhedra can be con- bia University. They were used in the mathe-
tinuously deformed into the sphere, so there is matics department but now are kept in a
a simple closed surface into which the "Hepta- cupboard in the Low Library, where nobody
hedron" can be deformed. This is the "Roman ever sees them.
Surface" investigated by Steiner.' In this
country it is called the 'Steiner Surface'. * All quotes are from Geometry and the Imagination by
Transparent material was chosen to make the David Hilbert and S. Cohn-Vossen.
form easy to comprehend.
[Ruth Vollmer recently exhibited at Betty Parsons Gal-
A separate wire circle can be leaned against lery, New York. Illustrations are courtesy Betty Parsons
the sides of any Steiner Surface—or its circular Gallery.

Tangents 1970
Clear acrylic. Height 18 in.
2
Spherical Tetrahedron 1970
Spun bronze. Height 12 in.
3
Construction Drawing of Pseudosphere 1970
10 x 32 in. Total length Pseudosphere 20 in.
4
Pseudosphere 1970
Laminated wood 10 X 24 in.
5
Heptahedron 1970
Brown opaque and transparent acrylic. Height 12 in.
6
Steiner Form 1970
Grey transparent Plexiglas. Height 12 in.
7
Three Axis and Four Rings 1970
Brass wire. Height 12 in.