- Designer: Koos Verhoeff (mathematician, computer scientist, mathematical artist)
- Location: Klaus Tschira Platz, near Im Neuenheimer Feld 231, 69120 Heidelberg, Germany
- Installation Date: 23 October 2015
- Tom Verhoeff, Koos Verhoeff.
"
**Three Mathematical Sculptures for the Mathematikon**".*Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture*, pp.105-110, 2016.

[ Slides ]

- Mathemical Inspiration: The octahedron (the Platonic solid with 8 triangular faces), via an Euler cycle
- Origin of Name:
*Lobke*is an archaic/affective diminuitive of the Dutch word "lob", which means "lobe"; the sculpture has six "lobes" - Height: 3.5 m
- Mass: approx. 1200 kg
- Material: Stainless Steel (AISI 316), polished and glass-bead blasted
- Parts: Six conical segments
- Symmetry group:
***223**(Orbifold notation); 12 symmetries; achiral- order-3 (120-degree) rotational symmetry about vertical axis
- 60-degree rotoreflective symmetry about vertical axis
- mirror symmetric in three vertical planes

- Mathematical Construction:
Tom Verhoeff, Koos Verhoeff. "

**Lobke, and Other Constructions from Conical Segments**". In: Gary Greenfield, George Hart and Reza Sarhangi (Eds.),*Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture*, Tessellations Publishing, ISBN 978-1-938664-11-3, pp.309-316, August 2014.

[ Slides | Additional material ]

- Mathemical Inspiration: The figure-eight knot, via an embedding in the body-centered cubic lattice
- Origin of Name: All beams have been rotated along their longitudinal axis, so that the sculpture will balance on a single beam when it stands freely
- Diameter: 2.4 m
- Mass: approx. 350 kg
- Material: Stainless Steel (AISI 316), polished
- Parts: 16 beams, triangular cross section (triangle side length 40 cm),
connected by regular miter joints
All joint angles equal ≈109.5 degrees; all torsion angles equal 60 degrees (plus or minus); total torsion is zero

The vertices have integer coordinates; beam directions are the main diagonals of the cube (body-centered cubic lattice)

- Symmetry group (of center line):
**2x**(Orbifold notation); 4 symmetries; achiral- order-2 (180-degree) rotational symmetry
- ±90-degree rotoreflective symmetry

- Mathematical Construction:
Tom Verhoeff. "3D Turtle Geometry: Artwork, Theory, Program Equivalence and Symmetry".

*Int. J. of Arts and Technology*,**3**(2/3):288-319 (2010).

[ Full Text in TU/e Library (campus only) | Slides ]

- Mathematical Inspriration: The truncated icosahedron, via a Hamiltonian cycle
- Origin of Name: The football (Am. Eng. soccer ball) is traditionally covered with the faces of a truncated icosahedron, which has 32 faces (12 pentagons and 20 hexagons), 30 vertices, and 90 edges; it admits several Hamiltonian cycles; this is the most symmetric one
- Diameter: 2.4 m
- Mass: approx. 350 kg
- Material: Stainless Steel (AISI 316), glass-bead blasted
- Parts: 30 beams, square cross section (square side length 15 cm), connected by regular miter joints
- Symmetry group (of center line):
**223**(Orbifold notation); 6 symmetries; chiral- order-3 (120-degree) rotational symmetry about vertical axis
- 60-degree rotoreflective symmetry about vertical axis

- About
**miter joints**:Tom Verhoeff, Koos Verhoeff. "The Mathematics of Mitering and Its Artful Application". Appeared in

*Bridges Leeuwarden: Mathematical Connections in Art, Music, and Science*, Proceedings of the Eleventh Annual Bridges Conference, in Leeuwarden, The Netherlands, pp.225-234, July 2008.

Also see related Wolfram Mathematica Demonstrations (Mathematica or free CDF Player required): - Construction company: Roestvrijstaalindustrie Geton (Geton Stainless Steel Industry), Veldhoven, Netherlands
- Funding: Klaus Tschira Foundation