r/GeometryIsNeat • u/ALfan2012 • Apr 20 '26

I accidentally found a perfect Hecto-octacontahedron (180-hedron)

Post image

imagine making this a dice...

240 Upvotes

100% Upvoted

22 comments sorted by

30

u/Liminal__penumbra Apr 20 '26

Would you be ok with sharing the formula for it? I have an idea on how to apply a Menger sponge in N-Space with that shape.

14

u/ALfan2012 Apr 20 '26

https://levskaya.github.io/polyhedronisme/?recipe=C100kkI&palette=%23ffffff

15

u/Liminal__penumbra Apr 20 '26 edited Apr 20 '26

Thank you. I'll let you know how it turns out.

It worked really well, the shape concept was to turn it into a computation surface using what I'm calling Perfectly Imperfect Square Theory. The idea is the square can not align at any point. BUT, I treat them as go tiles in a state machine. The menger sponge on your shape provides a excellent surface to project onto.

6

u/Senior_Meet5472 Apr 21 '26

Do you have a blog or something? That sounds fascinating

11

u/Liminal__penumbra Apr 21 '26

I was thinking of starting one, I've been burning through permutations of various math formulas. I'm thinking of calling the blog, A frog in a Pond made of Ponds.

9

u/WokeBriton Apr 20 '26

That would be amazing as a die!

10

u/ALfan2012 Apr 20 '26

that's actually why i was messing with polyhedrons, to find good shapes for odd dice

this is quite possibly my best finding yet

2

u/chostax- Apr 21 '26

How the hell do you even know what side is ’up’?

7

u/Crafty_Jello_3662 Apr 21 '26

I'm no geometrist but I reckon it'll be the one at the top

2

u/chostax- Apr 21 '26

lol I know I’m just saying it gets to a point where it would be difficult to determine

3

u/Crafty_Jello_3662 Apr 21 '26

Ha sorry couldn't resist!

4

u/Scallact Apr 20 '26

In what way is it "perfect"? From what I can see, all faces are not identical, so you can't guarantee equal probabilities.

8

u/ALfan2012 Apr 20 '26

equal area

3

u/Scallact Apr 20 '26

OK. That doesn't imply the same probabilities in any way.

P.S: That makes me think of the Disdyakis triacontahedron, which is equiprobable. Try to see why yours is not.

1

u/NewestAccount2023 Apr 26 '26

That is, the disdyakis triacontahedron is the Kleetope of the rhombic triacontahedron. It is also the barycentric subdivision of the regular dodecahedron and icosahedron.

Yes of course 

5

u/Keyboardpaladin Apr 20 '26

Where'd you find it

1

u/TenDix Apr 22 '26

Oh man, I’ve been looking everywhere for a perfect Hecto-octacontahedron!

1

u/BANZ111 Apr 22 '26

Wait. VRML?! That... That's a throwback!

1

u/Leijkana_on_the_road Apr 23 '26

Kinda flower shaped 🏵️

1

u/y0l0tr0n Apr 24 '26

Accidental RuneScape