## Geometrikum - geometric exhibits to explore on the 3rd floor of Science Park 2

Hyperboloid of revolution -
Hyperbolic plane -
Klein bottle -
Menger Sponge -
Oloid -
Sierpinski tetrahedron -
Stanford bunny -
Villarceau circles --
Various

###### Villarceau circles

In geometry, Villarceau circles are a pair of circles produced by cutting a torus obliquely through the center at a special angle
(from Wikipedia).

Construction period: May 2016 - July 2016, more details here.

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###### Stanford bunny

We built the Stanford bunny out of Lego pieces for the
long night of science 2016.

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###### Hyperboloid of revolution

A hyperboloid of revolution of one sheet. The strings are straight lines. For any point on the surface, there are two straight lines lying entirely on the surface which pass through the point. This illustrates the doubly ruled nature of this surface.
From Wikipedia

Construction period: Feb. 2015 - March 2015, more details here.

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###### Menger Sponge and vice versa, card cubes

In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of the Cantor set and Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension, see Wikipedia.

Instructions from the
institute for figuring.
Card cube instructions.

Construction period: May 2014 - July 2014. No glue was used!
More details here.

###### Menger Sponge, perler beads

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###### A Sierpinski Tetrahedron made of straws

was built during the long night of science 2014.

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###### Hyperbolic plane

2013, more information of the
discoverer of hyperbolic crochet Daina Taimina
on the homepage of the Crochet Coral Reef project.

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###### Grid of Klein bottle made of cable ties

2017

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###### Oloid

An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle. The distance between the circle centers equals the radius of the circles. One third of each circle's perimeter lies inside the convex hull, so the same shape may be also formed as the convex hull of the two remaining circular arcs each spanning an angle of 4π/3.
From Wikipedia

Construction period: Autumn 2017.

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###### Match Cube - Match Circle

2014, 2017, no glue was used!

Match Circle - they see me rolling

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###### Paper works

including a 12-unit stellated octahedron and a 30-unit stellated icosahedron made of Sonobe modules, furthermore, a truncated icosahedron.

No glue was used!

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Johannes Kepler Universität Linz,
Institut für Angewandte Geometrie, Altenberger Str.69, 4040 Linz