Poincaré Dodecahedron principle
Poincaré Dodecahedron principle from Renate Quehenberger on Vimeo.
This example shows the principle of the Poincaré Dodecahedron applied on the 2 epitahedra filling the dodecahedron performing counter-rotation in 10 steps instead of the 2D pentagon counter-rotation suggested by Henri Poincaré (1904) .
Poincaré Epita-Dodecahedron
Poincaré Epita_Dodecahedron mov12 from Renate Quehenberger on Vimeo.
This visualization demonstrates the 12 steps of counter-rotating pentagons in the dodecahedron based upon Henri Poincaré’s description (1904).
The pattern evolves from the 12 epitahedra,- found by R. Quehenberger (2006) – filling the dodecahedron with intersecting apexes.
CAD modeling and 3D animated geometry by Christian Magnes
script by Renate Quehenberger
QC Epitahedron Examples
The epitahedron, a golden hexahedron, found by Renate Quehenberger 2006
a 3D version of a 5D unit cell shows hyper-Platonic properties by constructing platonic
solids in a higher dimensional view
3D animated geometry methods allow to indicate symmetries
Geometry by Renate Quehenberger
Programming: Dr. Hans Katzgraber
3D modeling and animation by Christian Magnes
mentoring: Peter Weibel
QC Epitahedron Examples H264 from Renate Quehenberger on Vimeo.
Studies: 4π evolution of e
Logarithmic spirals evolvement in 3D space
inspired by formulas in statistical thermodynamics (Erwin Schrödinger)
for further analysis
Artist: Nikola Tasic
4pi evolution of e from Renate Quehenberger on Vimeo.
Emergent Structures
Studies of symmetries emerging from a five-vector
establishing a wave-field in 5 different directions of space.
Artist: Rudi Friemel
Emergent Structures from Renate Quehenberger on Vimeo.