[math-fun] Unseasonal decorations
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static) Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron! Aren't you glad you asked ... WFL
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course. To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices) On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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Neil, Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work! But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable. If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)? Fred On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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Howzat? [ 0, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 0, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 0, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ] WFL On 1/5/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neil,
Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work!
But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable.
If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)?
Fred
On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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Er, out! Try instead [ 1, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 1, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 1, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ] WFL On 1/6/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Howzat?
[ 0, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 0, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 0, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ]
WFL
On 1/5/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neil,
Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work!
But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable.
If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)?
Fred
On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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Fred, That's great! and all three are new to the OEIS. How shall I describe this polytope - name, description, source, references, whatever is appropriate? And can you send me a picture I can attach to the sequences? (I could take a screen shot from the gif in your initial message, but you may have something better) Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Mon, Jan 6, 2020 at 2:33 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Howzat?
[ 0, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 0, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 0, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ]
WFL
On 1/5/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neil,
Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work!
But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable.
If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)?
Fred
On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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Output needs to be at the start of my loop instead of the end! Third time lucky ... [ 1, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1 ] [ 1, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1 ] [ 1, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1 ] References & graphics --- https://en.wikipedia.org/wiki/Rhombic_enneacontahedron George W. Hart untitled notes: zonohedra; triacontahedral & enneacontahedral rhomboid packings http://www.georgehart.com/dissect-re/dissect-re.htm WFL On 1/6/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, That's great! and all three are new to the OEIS.
How shall I describe this polytope - name, description, source, references, whatever is appropriate? And can you send me a picture I can attach to the sequences? (I could take a screen shot from the gif in your initial message, but you may have something better)
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Mon, Jan 6, 2020 at 2:33 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Howzat?
[ 0, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 0, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 0, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ]
WFL
On 1/5/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neil,
Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work!
But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable.
If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)?
Fred
On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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Fred, Thank you very much! Your three sequences are now A330566, -567, and -568. The OEIS has some higher-dimensional examples, including many of my favorite lattice packings (to get the graph, join each point to the nearest points). For the Leech lattice in 24D, I could only get three terms: 1, 196560, 39462040800 - see A323282. The E_8 lattice is a lot easier and is known explicitly, see A008340. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Mon, Jan 6, 2020 at 3:27 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Output needs to be at the start of my loop instead of the end! Third time lucky ...
[ 1, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1 ] [ 1, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1 ] [ 1, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1 ]
References & graphics ---
https://en.wikipedia.org/wiki/Rhombic_enneacontahedron
George W. Hart untitled notes: zonohedra; triacontahedral & enneacontahedral rhomboid packings http://www.georgehart.com/dissect-re/dissect-re.htm
WFL
On 1/6/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, That's great! and all three are new to the OEIS.
How shall I describe this polytope - name, description, source, references, whatever is appropriate? And can you send me a picture I can attach to the sequences? (I could take a screen shot from the gif in your initial message, but you may have something better)
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Mon, Jan 6, 2020 at 2:33 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Howzat?
[ 0, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 0, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 0, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ]
WFL
On 1/5/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neil,
Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work!
But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable.
If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)?
Fred
On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation ---
https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif
(ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
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In the existing OEIS examples, the first number in a CS is always 1 (there's exactly 1 vertex at distance 0, namely the vertex itself), and there are no trailing 0 entries. Fred Lunnon writes:
Howzat?
[ 0, 3, 11, 8, 18, 10, 18, 8, 11, 3, 1, 0 ] [ 0, 5, 5, 15, 10, 20, 10, 15, 5, 5, 1, 0 ] [ 0, 6, 6, 15, 9, 18, 9, 15, 6, 6, 1, 0 ]
WFL
On 1/5/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neil,
Actual vertices number 20x 6-valent + 12x 5-valent + 60x 3-valent --- emphasising that the 3 CS's might prove manually quite hard work!
But as it happens, a Magma tool I developed for the (substantial) project associated with that video facilitates building the polyhedral boundary 1-skeleton, from which CS would be easily derivable.
If you already have software for latter, do you want the graph --- say, as a list of pairs of integers (vertices)?
Fred
On 1/5/20, Neil Sloane <njasloane@gmail.com> wrote:
Fred, nice pics! For the first one, Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif can you get me the two coordination sequences? It looks like there are two kinds of vertices, trivalent and pentavalent, so there will be two sequences, both finite of course.
To see what I mean, look at https://oeis.org/A330564, where I did the small stellated dodecahedron, which has pentavalent and trivalent vertices. Or A329500, where I did the truncated icosahedron or Buckyball (which only has trivalent vertices)
On Sun, Jan 5, 2020 at 3:17 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Tardy Christmas tree bauble, or maybe New Year detonation --- https://www.dropbox.com/s/6uiwzac2rwaoqwu/enneaconta_movie.8.gif (ignore any pop-ups; open in browser if static)
Delayed owing to a technical hitch while packing polytope: see https://www.dropbox.com/s/otp534dy9gye0in/enneaconta_evert.gif Is it Anish Kapoor's latest wheeze to make Orbits great again? A fairground carousel with elf & sleighty issues? A wrecked novelty umbrella? No --- it's an everted enneacontahedron!
Aren't you glad you asked ... WFL
participants (3)
-
Fred Lunnon -
Neil Sloane -
Tom Karzes