Geometry


Mobius Strips | Knots | Menger & Sierpinski Objects | Polyhedron Constructions | Curious Solids | Borromean Rings | Labyrinths & Mazes

Mobius Strips

Six centres of rotation so that each block moves to the position of its neighbour

 

A torus whose square cross-section is also rotated 90° around its own axis


Knots

A separate page of simple tubular knots is here.

3.1 variations of my own

A badly edited version of the image marked † appeared in What Are You Looking At?, Carlton, 2005, and Fantastic Optical Illusions, Carlton, 2006. This pattern shows effects of the Hermann Grid.


Menger & Sierpinski Objects

Menger Carpet / Sierpinski Gasket

Menger Cube

Inverse Menger Cube

Sierpinski Cube

Sierpinski Tetrahedron

Sierpinski Pyramid


Polyhedron Constructions

Dodecahedron Cubes

Internal Hedrons

Creating an inner polyhedron from the polygonal mid-points leads to an infinite zoom alternating between pairs: Cube/Octahedron, Dodecahedron/Icosahedron, Tetrahedron/Tetrahedron.


Curious Solids

An object formed from the perpendicular intersection of three coloured cylinders : seen in X, Y, Z, three angular views, and two animations.

A rhombic dodechedron (rather than the familiar type made from regular pentagons) : seen in X, Y, Z, three angular views, and two animations.


Borromean Rings

Any single ring can pass through the loop of any other, as a pair, but all three remain as a knot : seen in X, Y, Z, and one angular view.

The rectangular version interlocks in such a way as to resemble a Chinese wooden puzzle, though in this case there is no solution.


Labyrinths & Mazes

'Rites-Of-Passage' Paths

 

Roman Design

 

Freher's Paradoxical Emblems, #113
This one is different in that the path is on top of the walls rather than between them, and it isn't a true labyrinth as there are two directions to each successive inner level.

 

Edward Gorey's The Awdrey-Gore Legacy

 

Miscellaneous


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