Any Names for Cubes of more than 4-dimensions?
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So, when you look at shapes that are projected into dimensions higher than 3, the most famous example from what I've seen is the cube. The n-dimensional hypercube has been theorized in higher dimensions so much, that the 4-dimensional hypercube has a name, it is called the tesseract. So, let's say I wanted to project a cube beyond 4 spatial dimensions, what would the cube be known as in 5,6,7,etc. dimensions? Are there any special names?
projective-geometry
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
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show 3 more comments
$begingroup$
So, when you look at shapes that are projected into dimensions higher than 3, the most famous example from what I've seen is the cube. The n-dimensional hypercube has been theorized in higher dimensions so much, that the 4-dimensional hypercube has a name, it is called the tesseract. So, let's say I wanted to project a cube beyond 4 spatial dimensions, what would the cube be known as in 5,6,7,etc. dimensions? Are there any special names?
projective-geometry
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
$endgroup$
$begingroup$
I think its called the "Hilbert Cube"
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– glowstonetrees
Dec 1 '18 at 19:57
$begingroup$
Okay, I'll look it up
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– Xavier Stanton
Dec 1 '18 at 19:58
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The tesseract is not a hypercube; it's what you get by flattening a 4D hypercube into 3D, just as flattening a cube into 2D gives 6 squares.
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– J.G.
Dec 1 '18 at 20:08
1
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@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
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– timtfj
Dec 1 '18 at 20:51
1
$begingroup$
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
$endgroup$
– Morgan Rodgers
Dec 2 '18 at 0:20
|
show 3 more comments
$begingroup$
So, when you look at shapes that are projected into dimensions higher than 3, the most famous example from what I've seen is the cube. The n-dimensional hypercube has been theorized in higher dimensions so much, that the 4-dimensional hypercube has a name, it is called the tesseract. So, let's say I wanted to project a cube beyond 4 spatial dimensions, what would the cube be known as in 5,6,7,etc. dimensions? Are there any special names?
projective-geometry
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
$endgroup$
So, when you look at shapes that are projected into dimensions higher than 3, the most famous example from what I've seen is the cube. The n-dimensional hypercube has been theorized in higher dimensions so much, that the 4-dimensional hypercube has a name, it is called the tesseract. So, let's say I wanted to project a cube beyond 4 spatial dimensions, what would the cube be known as in 5,6,7,etc. dimensions? Are there any special names?
projective-geometry
projective-geometry
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
edited Dec 2 '18 at 0:20
Morgan Rodgers
9,59221439
9,59221439
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
asked Dec 1 '18 at 19:52
Xavier StantonXavier Stanton
311211
311211
$begingroup$
I think its called the "Hilbert Cube"
$endgroup$
– glowstonetrees
Dec 1 '18 at 19:57
$begingroup$
Okay, I'll look it up
$endgroup$
– Xavier Stanton
Dec 1 '18 at 19:58
$begingroup$
The tesseract is not a hypercube; it's what you get by flattening a 4D hypercube into 3D, just as flattening a cube into 2D gives 6 squares.
$endgroup$
– J.G.
Dec 1 '18 at 20:08
1
$begingroup$
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
$endgroup$
– timtfj
Dec 1 '18 at 20:51
1
$begingroup$
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
$endgroup$
– Morgan Rodgers
Dec 2 '18 at 0:20
|
show 3 more comments
$begingroup$
I think its called the "Hilbert Cube"
$endgroup$
– glowstonetrees
Dec 1 '18 at 19:57
$begingroup$
Okay, I'll look it up
$endgroup$
– Xavier Stanton
Dec 1 '18 at 19:58
$begingroup$
The tesseract is not a hypercube; it's what you get by flattening a 4D hypercube into 3D, just as flattening a cube into 2D gives 6 squares.
$endgroup$
– J.G.
Dec 1 '18 at 20:08
1
$begingroup$
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
$endgroup$
– timtfj
Dec 1 '18 at 20:51
1
$begingroup$
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
$endgroup$
– Morgan Rodgers
Dec 2 '18 at 0:20
$begingroup$
I think its called the "Hilbert Cube"
$endgroup$
– glowstonetrees
Dec 1 '18 at 19:57
$begingroup$
I think its called the "Hilbert Cube"
$endgroup$
– glowstonetrees
Dec 1 '18 at 19:57
$begingroup$
Okay, I'll look it up
$endgroup$
– Xavier Stanton
Dec 1 '18 at 19:58
$begingroup$
Okay, I'll look it up
$endgroup$
– Xavier Stanton
Dec 1 '18 at 19:58
$begingroup$
The tesseract is not a hypercube; it's what you get by flattening a 4D hypercube into 3D, just as flattening a cube into 2D gives 6 squares.
$endgroup$
– J.G.
Dec 1 '18 at 20:08
$begingroup$
The tesseract is not a hypercube; it's what you get by flattening a 4D hypercube into 3D, just as flattening a cube into 2D gives 6 squares.
$endgroup$
– J.G.
Dec 1 '18 at 20:08
1
1
$begingroup$
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
$endgroup$
– timtfj
Dec 1 '18 at 20:51
$begingroup$
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
$endgroup$
– timtfj
Dec 1 '18 at 20:51
1
1
$begingroup$
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
$endgroup$
– Morgan Rodgers
Dec 2 '18 at 0:20
$begingroup$
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
$endgroup$
– Morgan Rodgers
Dec 2 '18 at 0:20
|
show 3 more comments
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$begingroup$
I think its called the "Hilbert Cube"
$endgroup$
– glowstonetrees
Dec 1 '18 at 19:57
$begingroup$
Okay, I'll look it up
$endgroup$
– Xavier Stanton
Dec 1 '18 at 19:58
$begingroup$
The tesseract is not a hypercube; it's what you get by flattening a 4D hypercube into 3D, just as flattening a cube into 2D gives 6 squares.
$endgroup$
– J.G.
Dec 1 '18 at 20:08
1
$begingroup$
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
$endgroup$
– timtfj
Dec 1 '18 at 20:51
1
$begingroup$
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
$endgroup$
– Morgan Rodgers
Dec 2 '18 at 0:20