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







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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
















0












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    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














0












0








0





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 2 '18 at 0:20









Morgan Rodgers

9,59221439




9,59221439










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


















  • $begingroup$
    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










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