Topological Nets that Overlap

Klein Surfaces

[Making Math Models] > [Topological Nets] > [Klein Surfaces]

Klein surfaces are inspired by the Klein bottle first described by mathematician Felix Klein in the 19th century. For the saucer like structures below the tubes of the Klein bottle are reduced to singular polyhedron surrounded by an annuloid. Other examples have radial tubes for the tessellating varieties and linear tubes for the linear surfaces.

An assembled topological net for a Klein surface in the shape of a saucer built with triangles, squares and octagons.

structure: Kepler-Klein monosurface

components: triangles, squares, octagons

An assembled topological net for a Klein surface in the shape of a saucer built with triangles, squares and hexagons.

structure: Kepler-Klein monosurface

components: triangles, squares, hexagons

An assembled topological net for a Klein surface in the shape of a saucer built with triangles, squares and pentagons.

structure: Kepler-Klein monosurface

components: triangles, squares, pentagons

An assembled topological net for a Klein surface in the shape of a saucer built with squares, hexagons, and decagons.

structure: Kepler-Klein monosurface

components: squares, hexagons, dodecagons

An assembled topological net for a Klein surface in the shape of a saucer built with squares, pentagons, and icosagons.

structure: Kepler-Klein monosurface

components: squares, pentagons, icosagons

An assembled topological net for a Klein surface in the shape of a saucer built with triangles and squares.

structure: Kepler-Klein monosurface

components: triangles, squares

An assembled topological net for a Kepler-Klein surface built with hexagons.

structure: Kepler-Klein monosurface

components: squares, hexagons

An assembled topological net for a Kepler-Klein surface built with squares, hexagons, and dodecagons.

structure: Kepler-Klein monosurface

components: squares, hexagons, dodecagons

An assembled topological net for a Kepler-Klein surface built with triangles, squares, and hexagons.

structure: Kepler-Klein monosurface

components: triangles, squares, hexagons

An assembled topological net for a Kepler-Klein surface built with triangles, squares, and hexagons.

structure: Kepler-Klein monosurface

components: triangles, squares, hexagons

An assembled topological net for a Kepler-Klein surface built with squares, pentagons, and decagons.

structure: Kepler-Klein monosurface

components: squares, pentagons, decagons

An assembled topological net for a Kepler-Klein surface built with squares.

structure: Kepler-Klein monosurface

components: squares

An assembled topological net for a Kepler-Klein hemicubic surface built with squares.

structure: Klein hemicubic monosurface

components: squares

An assembled topological net for a Kepler-Klein cyclinder surface built with squares.

structure: Klein cyclinder monosurface

components: squares

An assembled topological net for a Kepler-Klein surface in the shape of a saucer built with pentagons.

structure: Kepler-Klein monosurface

components: triangles, pentagons

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