Topological Nets that Overlap

Handlehedra

[Making Math Models] > [Topological Nets] > [Handlehedra]

Handleheda are inspired by handle spheres from geometric topology. In structural geometric topologuy they become polyhedral analogues. Handlehedra begin with Kepler handleoids like the one below and to the right. They are then attached by their handles. In the case of paper models, they are glued. Each of the models below are assembled in the same manner.

Assembled Kepler dodecahedral handlehedron

12 Kepler handleoids folded and attached

at their handles make the handlehedron to the left.

An assembled topological net for a dodecahedral handlehedron like a handle sphere built with pentagons.

structure: Kepler dodecahedral handlehedron

components: pentagons

An assembled topological net for a dodecahedral handlehedron like a handle sphere built with pentagons.

structure: Kepler dodecahedral handlehedron

components: pentagons

An assembled topological net for a tetrahedral handlehedron like a handle sphere built with squares and hexagons.

structure: Kepler tetrahedral handlehedron

components: squares, hexagons

An assembled topological net for a tetrahedral handlehedron like a handle sphere built with hexagons.

structure: Kepler tetrahedral handlehedron

components: hexagons

An assembled topological net for a cubic handlehedron like a handle sphere built with octagons.

structure: Kepler cubic handlehedron

components: octagons

An assembled topological net for a tetrahedral handlehedron like a handle sphere built with triangles and squares.

structure: Kepler tetrahedral handlehedron

components: triangles, squares

An assembled topological net for a dodecahedral handlehedron like a handle sphere built with squares and pentagons.

structure: Kepler dodecahedral handlehedron

components: squares, pentagons

An assembled topological net for a dodecahedral handlehedron like a handle sphere built with pentagons.

structure: Kepler dodecahedral handlehedron

components: pentagons

An assembled topological net for a cubic handlehedron like a handle sphere built with squares and octagons.

structure: Kepler cubic handlehedron

components: squares, octagons

structure: Kepler icosahedral handlehedron

components: triangles, squares

structure: Kepler octahedral handlehedron

components: triangles, squares

structure: Kepler tetrahedral handlehedron

components: triangles, squares

structure: Kepler octahedral handlehedron

components: squares, hexagons

structure: Kepler dodecahedral handlehedron

components: squares, pentagons

structure: Kepler icosahedral handlehedron

components: squares, hexagons

structure: Kepler icosahedral handlehedron

components: triangles, squares

structure: Kepler icosahedral handlehedron

components: squares, hexagons, cubes, hexagonal prisms

Page updated

Google Sites

Report abuse