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Kepler-Klein surfaces are one-sided surfaces inspired by the annuloid studies of Johannes Kepler and the Klein bottle of mathematician Felix Klein. As such, they are all monosurfaces, meaning they have only one side. They are roughly classified by their geometric structure into four categories: points (Kepler-Klein saucers), lines (Kepler-Klein lines), planar surfaces (Kepler-Klein planes), and 3-dimensional surfaces (Kepler-Klein polysurfaces).Â
structure: Kepler-Klein saucer
components: triangles, squares, pentagons
structure: Kepler-Klein saucer
components: triangles, squares
structure: Kepler-Klein saucer
components: triangles, squares
structure: Kepler-Klein saucer
components: triangles
structure: Kepler-Klein saucer
components: triangles, hexagons
structure: Kepler-Klein saucer
components: triangles, dodecagons
structure: Kepler-Klein saucer
components: triangles, pentagons
structure: Kepler-Klein saucer
components: triangles, squares
structure: Kepler-Klein saucer
components: triangles, squares, hexagons
structure: Kepler-Klein saucer
components: triangles, octagons
structure: Kepler-Klein saucer
components: triangles, squares, hexagons
structure: Kepler-Klein saucer
components: triangles, squares, hexagons
structure: Kepler-Klein saucer
components: triangles, squares, hexagons
structure: Kepler-Klein saucer
components: triangles, squares, hexagons
structure: Kepler-Klein saucer
components: triangles, squares, octagons
structure: Kepler-Klein saucer
components: squares
structure: Kepler-Klein saucer
components: squares, pentagons, icosagons
structure: Kepler-Klein saucer
components: squares, hexagons, dodecagons
structure: Kepler-Klein saucer
components: squares, octagons
structure: Kepler-Klein saucer
components: squares, hexagons
structure: Kepler-Klein saucer
components: squares, octagons
structure: Kepler-Klein line
components: squares
structure: Kepler-Klein line
components: squares, hexagons
structure: Kepler-Klein line
components: squares, hexagons
structure: Kepler-Klein line
components: squares, octagons
structure: Kepler-Klein line
components: squares, pentagons, decagons
structure: Kepler-Klein line
components: squares, hexagons, dodecagons
structure: Kepler-Klein line
components: triangles, squares, hexagons
structure: Kepler-Klein line
components: triangles, squares
structure: Kepler-Klein line
components: triangles, squares, hexagons
structure: Kepler-Klein plane
components: squares, octagons
structure: Kepler-Klein plane
components: triangles, squares, hexagons
structure: Kepler-Klein plane
components: triangles, squares, hexagons
structure: Kepler-Klein plane
components: triangles, squares, hexagons
structure: Kepler-Klein plane
components: squares, hexagons, dodecagons
structure: Kepler-Klein plane
components: squares
structure: Klein cylinder
components: squaresÂ
structure: Kepler-Klein cubic polysurface
components: squares
structure: Kepler-Klein hemicubic triplane
components: squares
structure: Kepler-Klein cyliner polysurface
components: squares
structure: Kepler-Klein biplane
components: squares
structure: Kepler-Klein biplane
components: squares
structure: Kepler-Klein biplane
components: squares
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