Mattias Malmer pointed me at an interes

Tim Hutton - 2018-07-04 02:36:07+0000 - Updated: 2018-07-04 09:32:07+0000

Mattias Malmer pointed me at an interesting space-filling shape that I hadn't seen before, with curved faces.

It was discovered by an architect, Peter Pearce, in the 1960's. He called it the 'space filling bcc saddle tetrahedron'.

Packaging structure? Or a blueprint of space? | BEACH

Shared with: Public, Daniel Piker

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Daniel Piker - 2018-07-17 10:50:46+0000

Here's another neat space filling 'saddle polyhedron' - and you can also use it to half fill space, with the solid boundary forming one of Schwarz's periodic minimal surfaces - either the P or the D, depending which of the faces you match up!

gerdschroeder-turk.org/wp-content/uploads/2015/06/SchroederHyde_PDStarblock_Helix91_2003.pdf

Tim Hutton - 2018-07-17 14:54:40+0000

+Daniel Piker Oh wow, that's great, thank you for sending that. Now I'm wondering what other symmetric curved surfaces fill space.

Tim Hutton - 2018-07-17 15:23:25+0000 - Updated: 2018-07-17 15:34:19+0000

This (enormous and wonderful) page by Alan Schoen talks about both of these space-filling saddle polyhedra. He calls them TT (Fig. E2.25) and DET (Fig. E2.50).

Alan Schoen geometry

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