## What's you're favorite 4d toratope?

Discussion of shapes with curves and holes in various dimensions.

## What's you're favorite toratope?

Tesserect
1
14%
Glome
1
14%
Cubinder
0
Spheritorus
0
Duocylinder
2
29%
Tiger
2
29%
Spherinder
0
Torishphere
0
Torinder
0
Ditorus
1
14%

### What's you're favorite 4d toratope?

What is your favorite Toratope that is in 4d? My favorite Toratope is the Duocylinder because it is basically a 2d plane that curves back in on it self but it requires four spatial dimensions to curve back in on itself. The Duocylinder is strange in the sense that it is a surface that requires n+2 dimensions to curve back in on itself instead of n+1 dimensions to curve back in on itself. A Duocylinder is a square but unlike what we usually think of as a square it is a square that has no edges and which curves back in on itself.
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anderscolingustafson
Tetronian

Posts: 312
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### Re: What's you're favorite 4d toratope?

I voted for the glome, but not just any old glome... I have in mind the Hopf fibration, of which the duocylinder is the simplest discrete version, but you can build bigger regular polytwisters out of it, that consist of n torus-shaped manifolds that wrap around each other in a swirling way. The biggest regular polytwister is probably the icosahedral polytwister, consisting of 20 triangular torus-like things that wrap around each other and close up into a ball. You should see this thing in 4D, it's pretty impressive!
quickfur
Pentonian

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### Re: What's you're favorite 4d toratope?

I voted for tiger I consider it something of my child
Marek14
Pentonian

Posts: 1102
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### Re: What's you're favorite 4d toratope?

I voted for ditorus, because I remember imagining and visualising the sequence of torus, ditorus, tritorus, etc. long before learning about the tiger or that there were exactly 5+5 toratopes in 4D.

Keiji

Posts: 1962
Joined: Mon Nov 10, 2003 6:33 pm
Location: Torquay, England

### Re: What's you're favorite 4d toratope?

I'd have to say Tiger as well. It's a super cool shape that only begins to occur in 4D. Not to mention the strange concept of its two major radii and a single minor, and how it's built in 4D.
in search of combinatorial objects of finite extent
ICN5D
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### Re: What's you're favorite 4d toratope?

I would've voted for the tiger, except that I felt kinda let down when I eventually learned that it was nothing more than an "inflated" duocylinder ridge. Not that it's any less cool, mind you, but it's just that I expected a far more exotic shape, yet it turned out to be something "simple", or at least closely related to something very familiar to me -- the duocylinder.
quickfur
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