November 2015 – Page 2 – The Inner Frame

The Grand Gulch

Spring Break 1994 took me to Utah. After 24 hours in the car the landscape started to look like Max Ernst would have painted it.

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The entire week we (a group of eight members of CHAOS) would spend hiking through a large part of the Grand Gulch, a primitive area in the south eastern corner of Utah.

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This meant packing food for six days, and hoping that there would be enough water.

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Hiking through a canyon like this can be claustrophobic. After descending to the canyon floor, one is constantly surrounded by unclimbable walls, and the barren vegetation is little consolation.

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But of course the landscape is full of surprises, with new views at every turn. And then there are the Anasazi ruins.

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The Ancestral Puebloans (or Anasazi) were a large Native American civilization that disappeared after 1150 CE, likely due to a climate change. Not much is known about them, but in the Grand Gulch one can find their cliff dwellings and pictograms.
There are worse things to leave behind.

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Neovius surface (Algorithmic Geometry IV)

When the truncated octahedron tiles space, the diagonals of the hexagonal faces become part of a line configuration.

TruncatedOctahedronTiling

Following these lines we can build the bent rhombi that we encountered in Schwarz’ P-surface, but here we will focus on the more complicated bent octagons that weave around the square faces of the truncated octahedra. These serve as Plateau contours for another minimal surface, the Neovius surface, named after the Finnish mathematician Edvard Rudolf Neovius, a student of Hermann Amandus Schwarz.

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One can also fill each octagon with four copies of said bent rhombus to obtain an interesting polygonal version of the Neovius surface. Here are two such filled octagons aligned. Note that we have broken a rule: The four bent rhombi that fill the octagon are not rotated about their edges to fit together, but reflected.

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