What's the parametric equations of a hyperbolic dodecahedron?
$begingroup$
I was hoping someone could help me determine explicitly the
parameterized equations in 3D plane geometry (x,y,z) for a hyperbolic dodecahedron, and ideally the other hyperbolic form platonic solids Tetrahedron, Hexahedron [cube], and Icosahedron. I'm modeling them using MathMod and the programming language is in explicit parametric form. I'm not familiar with how to calculate the shapes in this way, but did find the hyperbolic octahedron in it's explicit parametric form, including it's intervals, using the mathworld-wolfram website [http://mathworld.wolfram.com/HyperbolicOctahedron.html], but the formulas weren't included in the other hyperbolic shapes.
How would I go about converting these shapes into this form?
parametric mathematical-modeling hyperbolic-geometry computational-geometry parametrization
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
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migrated from mathematica.stackexchange.com Jan 5 '18 at 9:18
This question came from our site for users of Wolfram Mathematica.
add a comment |
$begingroup$
I was hoping someone could help me determine explicitly the
parameterized equations in 3D plane geometry (x,y,z) for a hyperbolic dodecahedron, and ideally the other hyperbolic form platonic solids Tetrahedron, Hexahedron [cube], and Icosahedron. I'm modeling them using MathMod and the programming language is in explicit parametric form. I'm not familiar with how to calculate the shapes in this way, but did find the hyperbolic octahedron in it's explicit parametric form, including it's intervals, using the mathworld-wolfram website [http://mathworld.wolfram.com/HyperbolicOctahedron.html], but the formulas weren't included in the other hyperbolic shapes.
How would I go about converting these shapes into this form?
parametric mathematical-modeling hyperbolic-geometry computational-geometry parametrization
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
$endgroup$
migrated from mathematica.stackexchange.com Jan 5 '18 at 9:18
This question came from our site for users of Wolfram Mathematica.
$begingroup$
Look for the work of Igor Rivin. It may have the formulas you need.
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– toliveira
Jan 5 '18 at 10:49
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By the way, he himself uses this website! @IgorRivin
$endgroup$
– toliveira
Jan 5 '18 at 10:52
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I'm looking into his work, thanks. Actually, I noticed he's the referenced author of the hyperbolic dodecahedron graphic on the cited mathworld page in my OP.
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 11:37
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Does he give also for hyperbolic cube, icosahedron, etc. Is there a link?
$endgroup$
– Narasimham
Jan 5 '18 at 22:40
$begingroup$
He was referenced in the above mathworld.wolfram link in the OP and for the other hyperbolic shapes in the same site, but he's referenced for their graphical representions not for the parametric equations (of which only the hyperbolic octahedron has listed). "Rivin, I. "Hyperbolic Polyhedra Graphics." library.wolfram.com/infocenter/Demos/4558 "
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 22:54
add a comment |
$begingroup$
I was hoping someone could help me determine explicitly the
parameterized equations in 3D plane geometry (x,y,z) for a hyperbolic dodecahedron, and ideally the other hyperbolic form platonic solids Tetrahedron, Hexahedron [cube], and Icosahedron. I'm modeling them using MathMod and the programming language is in explicit parametric form. I'm not familiar with how to calculate the shapes in this way, but did find the hyperbolic octahedron in it's explicit parametric form, including it's intervals, using the mathworld-wolfram website [http://mathworld.wolfram.com/HyperbolicOctahedron.html], but the formulas weren't included in the other hyperbolic shapes.
How would I go about converting these shapes into this form?
parametric mathematical-modeling hyperbolic-geometry computational-geometry parametrization
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
$endgroup$
I was hoping someone could help me determine explicitly the
parameterized equations in 3D plane geometry (x,y,z) for a hyperbolic dodecahedron, and ideally the other hyperbolic form platonic solids Tetrahedron, Hexahedron [cube], and Icosahedron. I'm modeling them using MathMod and the programming language is in explicit parametric form. I'm not familiar with how to calculate the shapes in this way, but did find the hyperbolic octahedron in it's explicit parametric form, including it's intervals, using the mathworld-wolfram website [http://mathworld.wolfram.com/HyperbolicOctahedron.html], but the formulas weren't included in the other hyperbolic shapes.
How would I go about converting these shapes into this form?
parametric mathematical-modeling hyperbolic-geometry computational-geometry parametrization
parametric mathematical-modeling hyperbolic-geometry computational-geometry parametrization
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
edited Jan 5 '18 at 22:17
Du'uzu Mes
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
asked Jan 5 '18 at 8:49
Du'uzu MesDu'uzu Mes
135
135
migrated from mathematica.stackexchange.com Jan 5 '18 at 9:18
This question came from our site for users of Wolfram Mathematica.
migrated from mathematica.stackexchange.com Jan 5 '18 at 9:18
This question came from our site for users of Wolfram Mathematica.
$begingroup$
Look for the work of Igor Rivin. It may have the formulas you need.
$endgroup$
– toliveira
Jan 5 '18 at 10:49
$begingroup$
By the way, he himself uses this website! @IgorRivin
$endgroup$
– toliveira
Jan 5 '18 at 10:52
$begingroup$
I'm looking into his work, thanks. Actually, I noticed he's the referenced author of the hyperbolic dodecahedron graphic on the cited mathworld page in my OP.
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 11:37
$begingroup$
Does he give also for hyperbolic cube, icosahedron, etc. Is there a link?
$endgroup$
– Narasimham
Jan 5 '18 at 22:40
$begingroup$
He was referenced in the above mathworld.wolfram link in the OP and for the other hyperbolic shapes in the same site, but he's referenced for their graphical representions not for the parametric equations (of which only the hyperbolic octahedron has listed). "Rivin, I. "Hyperbolic Polyhedra Graphics." library.wolfram.com/infocenter/Demos/4558 "
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 22:54
add a comment |
$begingroup$
Look for the work of Igor Rivin. It may have the formulas you need.
$endgroup$
– toliveira
Jan 5 '18 at 10:49
$begingroup$
By the way, he himself uses this website! @IgorRivin
$endgroup$
– toliveira
Jan 5 '18 at 10:52
$begingroup$
I'm looking into his work, thanks. Actually, I noticed he's the referenced author of the hyperbolic dodecahedron graphic on the cited mathworld page in my OP.
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 11:37
$begingroup$
Does he give also for hyperbolic cube, icosahedron, etc. Is there a link?
$endgroup$
– Narasimham
Jan 5 '18 at 22:40
$begingroup$
He was referenced in the above mathworld.wolfram link in the OP and for the other hyperbolic shapes in the same site, but he's referenced for their graphical representions not for the parametric equations (of which only the hyperbolic octahedron has listed). "Rivin, I. "Hyperbolic Polyhedra Graphics." library.wolfram.com/infocenter/Demos/4558 "
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 22:54
$begingroup$
Look for the work of Igor Rivin. It may have the formulas you need.
$endgroup$
– toliveira
Jan 5 '18 at 10:49
$begingroup$
Look for the work of Igor Rivin. It may have the formulas you need.
$endgroup$
– toliveira
Jan 5 '18 at 10:49
$begingroup$
By the way, he himself uses this website! @IgorRivin
$endgroup$
– toliveira
Jan 5 '18 at 10:52
$begingroup$
By the way, he himself uses this website! @IgorRivin
$endgroup$
– toliveira
Jan 5 '18 at 10:52
$begingroup$
I'm looking into his work, thanks. Actually, I noticed he's the referenced author of the hyperbolic dodecahedron graphic on the cited mathworld page in my OP.
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 11:37
$begingroup$
I'm looking into his work, thanks. Actually, I noticed he's the referenced author of the hyperbolic dodecahedron graphic on the cited mathworld page in my OP.
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 11:37
$begingroup$
Does he give also for hyperbolic cube, icosahedron, etc. Is there a link?
$endgroup$
– Narasimham
Jan 5 '18 at 22:40
$begingroup$
Does he give also for hyperbolic cube, icosahedron, etc. Is there a link?
$endgroup$
– Narasimham
Jan 5 '18 at 22:40
$begingroup$
He was referenced in the above mathworld.wolfram link in the OP and for the other hyperbolic shapes in the same site, but he's referenced for their graphical representions not for the parametric equations (of which only the hyperbolic octahedron has listed). "Rivin, I. "Hyperbolic Polyhedra Graphics." library.wolfram.com/infocenter/Demos/4558 "
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 22:54
$begingroup$
He was referenced in the above mathworld.wolfram link in the OP and for the other hyperbolic shapes in the same site, but he's referenced for their graphical representions not for the parametric equations (of which only the hyperbolic octahedron has listed). "Rivin, I. "Hyperbolic Polyhedra Graphics." library.wolfram.com/infocenter/Demos/4558 "
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 22:54
add a comment |
1 Answer
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I was able to work out approximate parametric equations for a hyperbolic tetrahedron.
$x = (2cos(u) + 2cos^2(u) - 1)(1 - v)^2$
$y = (2sin(u) - 2sin(u)cos(u))(1 - v)^2$
$z = cos^3(v)$
Where u $in$ [-$pi$, $pi$] and v $in$ [0, 1]. Hope this helps.
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
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$begingroup$
I was able to work out approximate parametric equations for a hyperbolic tetrahedron.
$x = (2cos(u) + 2cos^2(u) - 1)(1 - v)^2$
$y = (2sin(u) - 2sin(u)cos(u))(1 - v)^2$
$z = cos^3(v)$
Where u $in$ [-$pi$, $pi$] and v $in$ [0, 1]. Hope this helps.
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
$endgroup$
add a comment |
$begingroup$
I was able to work out approximate parametric equations for a hyperbolic tetrahedron.
$x = (2cos(u) + 2cos^2(u) - 1)(1 - v)^2$
$y = (2sin(u) - 2sin(u)cos(u))(1 - v)^2$
$z = cos^3(v)$
Where u $in$ [-$pi$, $pi$] and v $in$ [0, 1]. Hope this helps.
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
$endgroup$
add a comment |
$begingroup$
I was able to work out approximate parametric equations for a hyperbolic tetrahedron.
$x = (2cos(u) + 2cos^2(u) - 1)(1 - v)^2$
$y = (2sin(u) - 2sin(u)cos(u))(1 - v)^2$
$z = cos^3(v)$
Where u $in$ [-$pi$, $pi$] and v $in$ [0, 1]. Hope this helps.
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
$endgroup$
I was able to work out approximate parametric equations for a hyperbolic tetrahedron.
$x = (2cos(u) + 2cos^2(u) - 1)(1 - v)^2$
$y = (2sin(u) - 2sin(u)cos(u))(1 - v)^2$
$z = cos^3(v)$
Where u $in$ [-$pi$, $pi$] and v $in$ [0, 1]. Hope this helps.
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
edited Dec 17 '18 at 18:44
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
answered Dec 12 '18 at 21:16
PharaohCola13PharaohCola13
14
14
add a comment |
add a comment |
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$begingroup$
Look for the work of Igor Rivin. It may have the formulas you need.
$endgroup$
– toliveira
Jan 5 '18 at 10:49
$begingroup$
By the way, he himself uses this website! @IgorRivin
$endgroup$
– toliveira
Jan 5 '18 at 10:52
$begingroup$
I'm looking into his work, thanks. Actually, I noticed he's the referenced author of the hyperbolic dodecahedron graphic on the cited mathworld page in my OP.
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 11:37
$begingroup$
Does he give also for hyperbolic cube, icosahedron, etc. Is there a link?
$endgroup$
– Narasimham
Jan 5 '18 at 22:40
$begingroup$
He was referenced in the above mathworld.wolfram link in the OP and for the other hyperbolic shapes in the same site, but he's referenced for their graphical representions not for the parametric equations (of which only the hyperbolic octahedron has listed). "Rivin, I. "Hyperbolic Polyhedra Graphics." library.wolfram.com/infocenter/Demos/4558 "
$endgroup$
– Du'uzu Mes
Jan 5 '18 at 22:54