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 at 0:20
Morgan Rodgers
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asked Dec 1 at 19:52
Xavier Stanton
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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 at 0:20
Morgan Rodgers
9,52421338
asked Dec 1 at 19:52
Xavier Stanton
292210
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I think its called the "Hilbert Cube"
– glowstonetrees
Dec 1 at 19:57
Okay, I'll look it up
– Xavier Stanton
Dec 1 at 19:58
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.
– J.G.
Dec 1 at 20:08
1
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
– timtfj
Dec 1 at 20:51
1
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
– Morgan Rodgers
Dec 2 at 0:20
|
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 at 0:20
Morgan Rodgers
9,52421338
asked Dec 1 at 19:52
Xavier Stanton
292210
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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 at 0:20
Morgan Rodgers
9,52421338
asked Dec 1 at 19:52
Xavier Stanton
292210
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Dec 2 at 0:20
Morgan Rodgers
9,52421338
asked Dec 1 at 19:52
Xavier Stanton
292210
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Dec 2 at 0:20
Morgan Rodgers
9,52421338
edited Dec 2 at 0:20
Morgan Rodgers
9,52421338
edited Dec 2 at 0:20
Morgan Rodgers
9,52421338
9,52421338
asked Dec 1 at 19:52
Xavier Stanton
292210
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 1 at 19:52
Xavier Stanton
292210
asked Dec 1 at 19:52
Xavier Stanton
292210
292210
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Xavier Stanton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I think its called the "Hilbert Cube"
– glowstonetrees
Dec 1 at 19:57
Okay, I'll look it up
– Xavier Stanton
Dec 1 at 19:58
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.
– J.G.
Dec 1 at 20:08
1
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
– timtfj
Dec 1 at 20:51
1
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
– Morgan Rodgers
Dec 2 at 0:20
|
show 3 more comments
I think its called the "Hilbert Cube"
– glowstonetrees
Dec 1 at 19:57
Okay, I'll look it up
– Xavier Stanton
Dec 1 at 19:58
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.
– J.G.
Dec 1 at 20:08
1
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
– timtfj
Dec 1 at 20:51
1
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
– Morgan Rodgers
Dec 2 at 0:20
I think its called the "Hilbert Cube"
– glowstonetrees
Dec 1 at 19:57
I think its called the "Hilbert Cube"
– glowstonetrees
Dec 1 at 19:57
Okay, I'll look it up
– Xavier Stanton
Dec 1 at 19:58
Okay, I'll look it up
– Xavier Stanton
Dec 1 at 19:58
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.
– J.G.
Dec 1 at 20:08
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.
– J.G.
Dec 1 at 20:08
1
1
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
– timtfj
Dec 1 at 20:51
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
– timtfj
Dec 1 at 20:51
1
1
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
– Morgan Rodgers
Dec 2 at 0:20
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
– Morgan Rodgers
Dec 2 at 0:20
|
show 3 more comments
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Xavier Stanton is a new contributor. Be nice, and check out our Code of Conduct.
Xavier Stanton is a new contributor. Be nice, and check out our Code of Conduct.
Xavier Stanton is a new contributor. Be nice, and check out our Code of Conduct.
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I think its called the "Hilbert Cube"
– glowstonetrees
Dec 1 at 19:57
Okay, I'll look it up
– Xavier Stanton
Dec 1 at 19:58
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.
– J.G.
Dec 1 at 20:08
1
@glowstonetrees Isn't the Hilbert cube infinite-dimensional with carefully chosen lengths?
– timtfj
Dec 1 at 20:51
1
It's just called an $n$-cube. It would just be confusing to have a different specialized name for each different $n$.
– Morgan Rodgers
Dec 2 at 0:20