Geometry

Geometry

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

Mobius Strips

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

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

Knots 3₁

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

Rotating gears inside a reflecting sphere.
Animation of the gears.
Some simple pieces of wood …
… which reduce to this.
Standard circular trefoil arrangement.
Square cutaway version.
Circular with a diamond pattern, also showing effects of Hermann Grid. †

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.

"There is no coming to the One with one jump, and none, without going about."
My variation with maze-like dead-ends and a single path to the centre.

Edward Gorey's The Awdrey-Gore Legacy

"The labyrinth at 3:27 after Miss Gentian had successfully found her way in and back."
"The labyrinth at 4:09 when Harold Tyne-Forque gave up trying to reach its heart."

Miscellaneous

Hans Vredeman de Vries
Corinthia
Hans Vredeman de Vries
This isn't quite right, but the original image was small and the perspective not very good.
A. Hill
Simple design found on a local building.

Sierpinski Objects

Square

Cube

Inverse Cube

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.

Curious Solids

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

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

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