Ray Tracing in odd spaces
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journey through Poincaré homology sphere
HenrikRuep
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The Poincaré homology sphere is obtained from a dodecahedron by identifying opposite faces with a suitable rotation. It has a canonical mectric with sectional curvature 1 a...
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A journey through a lens space
HenrikRuep
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A lense space is the quotient space of an special group operation of Z/n on a sphere (3-sphere in this case).
A fundamental domain is given by two intersecting planes in ...
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Euclidean space tesselated with cubes
HenrikRuep
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the Euclidean space is tesselated with cubes in the obvious way.
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Hyperbolic space tesselated with cubes
HenrikRuep
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the 3-dimensional Hyperbolic space is tesselated with cubes, so that at every vertex 12 cubes meet.
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Hyperbolic space tesselated with dodecahedrons
HenrikRuep
1,277 views
The 3-dimenional Hyperbolic space is tesselated with dodecahedrons, so that 12 of them meet at every vertex.
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tesselation of the 3-sphere with dodecahedrons
HenrikRuep
1,111 views
The 3 dimensional sphere is tesselated with dodecahedrons, os wht 4 dodecahedrons meet in each vertex. If one takes only one dodecahedron and identifies opposing faces rota...
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3-sphere tesselated with regular octahedrons
HenrikRuep
139 views
The 3 dimensional Sphere is tesselated with regular octahedrons. This is the only regular tesselation, that can be build with regular octahedrons.
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Hyperbolic space tesselated with dodecahedrons
HenrikRuep
339 views
the Hyperbolic space is tesselated with regular dodecahedrons. 8 of them meet in each vertex. Furthermore the edges form infinite straight lines.
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4D cube on a 3 sphere
HenrikRuep
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A 4D cube is placed in a 3-sphere. Then its vertices and edges and faces and hyperfaces are projected on the sphere. One yields a regular tesselation the 3 sphere with 3-cu...
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finest Tesselation of a 3-sphere with tetrahedron
HenrikRuep
412 views
The 3 sphere is tesselated with regular tetrahedrons. 12 of them meet at each vertex.
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