We are all very familiar with planar geometry – we see, for instance, a square or rectangle is a plain shape with all 4 corners being right angles (90 degrees). Curved space gets a LOT weirder:

It is possible, for instance, to construct a shape on a curved surface that has 5 (or even 6) corners, each having a right angle. Origami typically deals with sheets that start flat – a non-flat sheet affords fascinating properties.

After a conversation with Goran Konjevod (@foldsome), I wanted to try a technique he pioneered involving radially pleating such a non-Euclidean square.

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