there are 48 regular polyhedra
2,868,917
Published 2020-08-01
primary source: link.springer.com/article/10.1007%2FPL00009304
bgm: queerduckrecords.bandcamp.com/track/apeirohedron
visualization tool for the shapes in this video: cpjsmith.uk/regularpolyhedra
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conlangcritic.bandcamp.com/
seximal.net/
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janmisali.tumblr.com/
0:00 - introduction
1:06 - part one: what?
4:06 - part two: the platonic solids
6:21 - part three: the Kepler solids
9:00 - part four: the Kepler-Poinsot polyhedra
11:26 - part five: the regular tilings
13:15 - part six: the Petrie-Coxeter polyhedra
16:51 - part seven: the Petrials
21:08 - part eight: the blended apeirohedra
22:39 - part nine: the pure Grünbaum-Dress polyhedra
25:03 - part ten: summary
All Comments (20)
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plato: a regular polyhedron has equal edges and equal vertex angles diogenes: holds up infinite square tiling behold, a regular polyhedron
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17:02 "There's nothing in the definition that restricts polygons to two dimensions" Dear God
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my dad had the opposite reaction: i told him about the video and he said "why only 48?' i then told him the euclidean space restriction and he went "oh ok"
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Halfway I was laughing from the joy of discovery. By part 8 I was crying from the horror of discovery. By then, I felt like I was diving into an eldritch horror.
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For the people who read the comments first: A cube is made up of 4 hexagons.
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I never thought I would hear the words “dark geometry”
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I found the paper "Regular Polyhedra - Old And New" by Branko Grünbaum in 1977, which list all 47 regular polyhedra. The one that was found by Andreas Dress is the Skew Muoctahedron
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I would like to have it known that this video is responsible for one of my most “in character” moments of all time. My brand new girlfriend got in my car for the first time and said “Ooh! I get to find out what music you listen to.” All I could do was press play. At 23:30. This is not music. I was LISTENING to a video about Geometry while driving. I was listening to a video about DARK GEOMETRY while driving
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Thanks for being brave enough to stand up to Big Shape.
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Bart: There are 48 regular polyhedra. Homer: There are 48 regular polyhedra so far.
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I love how this is packed with easy-to-digest info distilled into half an hour but at the same time you can feel how deep Jan had to stare into the abyss to do that. Like, well done bro, you truly suffered for your art here!
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I’m in college learning more advanced math and computer science now, but I still come back to this video on occasion to keep myself humble.
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The moment you realise there are geometry Discord servers dealing in illegal polyhedra.
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This feels like a video that years from now will be the equivalent of what the "Turning a sphere inside-out" video became.
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The fact that this video codifies the names for some of the polyhedra it describes is amazing.
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One of my favorite sentences ever "The Petrial mutetrahedron can be derived either as the Petrie dual of the mutetrahedron or as a skew-dual of the dual of the Petrial halved mucube."
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“I’m making this for general audiences” 15 minutes later : D A R K G E O M E T R Y
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I'm actually astonished that this incredibly loose definition of a polyhedron does not lead to an infinite number of regular polyhedra.
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i like that all of these videos become utterly incomprehensible in the second half
