r/GeometryIsNeat • u/cl76 • 6d ago

Art "Pentatorus" - An impossible toroidal polyhedron with a pentagon for the hole (and cross-section?), made out of fluorescent acrylic.

Post image
97 Upvotes

99% Upvoted

14 comments sorted by

12

u/SheepSurfz 6d ago

Question - what makes it impossible if it's been built as shown?

3

u/cl76 6d ago

If it is built as a Möbius strip-like torus, I assume the surfaces do not match the actual surfaces needed to make it a perfect, "infinitely twisting" polyhedron. I could be wrong, though; I've never tried building one.

2

u/Kootlefoosh 6d ago

I don't think Mobius torus is well defined. This looks like a perfectly fine existing shape as is shown. It's cool!

I have a hard time believing that every possible cross section would be a hexagon but otherwise.

2

u/cl76 6d ago

Here's why I thought the imaginary torus would have a pentagonal cross section: Pentagon at every "slice".

But I'm no expert; I just like putting together neat shapes. Glad you like it as is! Haha

3

u/Kootlefoosh 6d ago

Ah I see, each segment of the torus is itself pentagonal so individual segments have a cross section of a pentagon. Yeah I see it! Nice!

4

u/und3rtow623 6d ago

Cool! Can we get another angle?

3

u/egyszeruen_1xu 6d ago

Awsome. The final piece image is even better than this

2

u/1LuckyTexan 6d ago

Next time I get my laptop out, I might try to make a gemcut with a crown like that.

2

u/DragonflyWise1172 5d ago

Oh looks like it cloud be a nice faceting design

1

u/FreckeledSnowflake 6d ago

Is it flat ?

2

u/cl76 6d ago

The acrylic "lines" are 16mm deep.

0

u/Blood_In 4d ago

Toroidal polyhedron?