[1/3] Here at Dehn’s Bakery, we bake all our cakes as perfect cubes. Of course, some customers prefer other rectangular prisms, and this morning we received an order for a cake with edges in the ratios 1:e:π. No problem! We just cut one of our cubes into these 28 pieces ...pic.twitter.com/3HqhZO6Ef9
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Replying to @gregeganSF
Do you have a description of each of the polyhedra this decomposition consists of I could play with, please?
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Replying to @graveolens
Greg Egan Retweeted Greg Egan
The description is in the 3rd tweet in the thread. With that recipe, you can construct the pieces for any edge ratios you like. The 2D dissections between rectangles of different ratios are shown here: https://twitter.com/gregeganSF/status/1174909329981358086 … illustrated with square/rect, but generalise easily.
Greg Egan added,
Greg Egan @gregeganSF[1/3] Here’s a dissection of a square into pieces that reassemble as a rectangle of any proportions [with the same area]. As@Ykulvaarlck pointed out in a comment to my previous thread, the construction I gave had some redundant cuts; here those cuts have been removed. pic.twitter.com/9O3S3jqVWcShow this thread1 reply 1 retweet 5 likes
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