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Don't forget my "old" homepage with considerable stuff to cylinder intersec=
tions.
http://www.baumanneduard.ch/
Best regards
Ed
----- Original Message -----=20
From: mananself@gmail.com [4D_Cubing]=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Monday, February 20, 2017 9:10 PM
Subject: [MC4D] Stellating intersection of cylinders
=20=20=20=20
Recently I saw these puzzles created by Alexandr Abalikhin (twistypuzzles=
ID: TER)
http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&act=3Dinv&key=3D784&off=
=3D0
http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&act=3Dinv&key=3D784&off=
=3D15
https://www.youtube.com/channel/UCUyPm2UVtP_GQloD4U7BVeQ
The puzzles with names including fourcylinder, sixcylinder, tricylinder i=
ntrigued me. Recently he constructed tencylinder puzzles:
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p361084
These puzzles are shape mods. But the shapes are very interesting. I cons=
ider them as different levels of stellation of the intersection of cylinder=
s.
The intersection of three orthogonal cylinders is well known and is a Ste=
inmetz Solid. He made this puzzle based on it:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5346
Then he extended the surfaces of the cylinders, until two meet, to get th=
is shape:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5605
You can think of the new shape as the region contained by at least two of=
the three cylinders. If you think of the original intersection as a "curvy=
" rhombic dodecahedron, then the new shape is a "curvy" stellated rhombic d=
odecahedron:
https://en.wikipedia.org/wiki/First_stellation_of_rhombic_dodecahedron
And Alexandr created stellations of intersections of more cylinders. I ca=
n see some corresponding "flat" stellated/compound polyhedra. But the curvy=
shapes are neat because one can construct them just out of cylinders.
I searched online, and only found pictures of the union or intersection o=
f cylinders, such as this page:
http://paulbourke.net/geometry/cylinders/
I haven't found anything about their stellations. Have mathematicians stu=
died them? Are the 11 shape s in this page a complete enumeration of the st=
ellations of 10 cylinders arranged in this manner?
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p361084
How many such shapes are out there?
Have you guys seen anything like this?
=20=20
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charset="UTF-8"
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=EF=BB=BF
Recently I saw these puzzles created by Alexandr Abalikhin (twistypuzz=
les=20
ID: TER)
p;key=3D784&off=3D0">http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&a=
mp;act=3Dinv&key=3D784&off=3D0
p;key=3D784&off=3D15">http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&=
amp;act=3Dinv&key=3D784&off=3D15
/www.youtube.com/channel/UCUyPm2UVtP_GQloD4U7BVeQ
The puzzles with names including fourcylinder, sixcylinder, tricylinde=
r=20
intrigued me. Recently he constructed tencylinder puzzles:
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p36=
1084
These puzzles are shape mods. But the shapes are very interesting. I=20
consider them as different levels of stellation of the intersection of=20
cylinders.
The intersection of three orthogonal cylinders is well known and is a=
=20
Steinmetz Solid. He made this puzzle based on it:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5346
Then he extended the surfaces of the cylinders, until two meet, to get=
this=20
shape:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5605
You can think of the new shape as the region contained by at least two=
of=20
the three cylinders. If you think of the original intersection as a "curv=
y"=20
rhombic dodecahedron, then the new shape is a "curvy" stellated rhombic=20
dodecahedron:
https://en.wikipedia.org/wiki/First_stellation_of_rhombic_dodecahedron=
And Alexandr created stellations of intersections of more cylinders. I=
can=20
see some corresponding "flat" stellated/compound polyhedra. But the curvy=
=20
shapes are neat because one can construct them just out of cylinders.
I searched online, and only found pictures of the union or intersectio=
n of=20
cylinders, such as this page:
http://paulbourke.net/geometry/cylinders/
I haven't found anything about their stellations. Have mathematicians=
=20
studied them? Are the 11 shape s in this page a complete enumeration of t=
he=20
stellations of 10 cylinders arranged in this manner?
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p36=
1084
How many such shapes are out there?
Have you guys seen anything like this?
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charset="UTF-8"
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Hi Nan,
I'm interested in
http://nan.ma/ElevenCell/index.html
why this not working?
Best regards
Ed
----- Original Message -----=20
From: mananself@gmail.com [4D_Cubing]=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Monday, February 20, 2017 9:10 PM
Subject: [MC4D] Stellating intersection of cylinders
=20=20=20=20
Recently I saw these puzzles created by Alexandr Abalikhin (twistypuzzles=
ID: TER)
http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&act=3Dinv&key=3D784&off=
=3D0
http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&act=3Dinv&key=3D784&off=
=3D15
https://www.youtube.com/channel/UCUyPm2UVtP_GQloD4U7BVeQ
The puzzles with names including fourcylinder, sixcylinder, tricylinder i=
ntrigued me. Recently he constructed tencylinder puzzles:
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p361084
These puzzles are shape mods. But the shapes are very interesting. I cons=
ider them as different levels of stellation of the intersection of cylinder=
s.
The intersection of three orthogonal cylinders is well known and is a Ste=
inmetz Solid. He made this puzzle based on it:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5346
Then he extended the surfaces of the cylinders, until two meet, to get th=
is shape:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5605
You can think of the new shape as the region contained by at least two of=
the three cylinders. If you think of the original intersection as a "curvy=
" rhombic dodecahedron, then the new shape is a "curvy" stellated rhombic d=
odecahedron:
https://en.wikipedia.org/wiki/First_stellation_of_rhombic_dodecahedron
And Alexandr created stellations of intersections of more cylinders. I ca=
n see some corresponding "flat" stellated/compound polyhedra. But the curvy=
shapes are neat because one can construct them just out of cylinders.
I searched online, and only found pictures of the union or intersection o=
f cylinders, such as this page:
http://paulbourke.net/geometry/cylinders/
I haven't found anything about their stellations. Have mathematicians stu=
died them? Are the 11 shape s in this page a complete enumeration of the st=
ellations of 10 cylinders arranged in this manner?
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p361084
How many such shapes are out there?
Have you guys seen anything like this?
=20=20
------=_NextPart_000_002D_01D28BCF.6FFC9100
Content-Type: text/html;
charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
=EF=BB=BF
Recently I saw these puzzles created by Alexandr Abalikhin (twistypuzz=
les=20
ID: TER)
p;key=3D784&off=3D0">http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&a=
mp;act=3Dinv&key=3D784&off=3D0
p;key=3D784&off=3D15">http://twistypuzzles.com/cgi-bin/pdb-search.cgi?&=
amp;act=3Dinv&key=3D784&off=3D15
/www.youtube.com/channel/UCUyPm2UVtP_GQloD4U7BVeQ
The puzzles with names including fourcylinder, sixcylinder, tricylinde=
r=20
intrigued me. Recently he constructed tencylinder puzzles:
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p36=
1084
These puzzles are shape mods. But the shapes are very interesting. I=20
consider them as different levels of stellation of the intersection of=20
cylinders.
The intersection of three orthogonal cylinders is well known and is a=
=20
Steinmetz Solid. He made this puzzle based on it:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5346
Then he extended the surfaces of the cylinders, until two meet, to get=
this=20
shape:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3D5605
You can think of the new shape as the region contained by at least two=
of=20
the three cylinders. If you think of the original intersection as a "curv=
y"=20
rhombic dodecahedron, then the new shape is a "curvy" stellated rhombic=20
dodecahedron:
https://en.wikipedia.org/wiki/First_stellation_of_rhombic_dodecahedron=
And Alexandr created stellations of intersections of more cylinders. I=
can=20
see some corresponding "flat" stellated/compound polyhedra. But the curvy=
=20
shapes are neat because one can construct them just out of cylinders.
I searched online, and only found pictures of the union or intersectio=
n of=20
cylinders, such as this page:
http://paulbourke.net/geometry/cylinders/
I haven't found anything about their stellations. Have mathematicians=
=20
studied them? Are the 11 shape s in this page a complete enumeration of t=
he=20
stellations of 10 cylinders arranged in this manner?
http://twistypuzzles.com/forum/viewtopic.php?f=3D15&p=3D361084#p36=
1084
How many such shapes are out there?
Have you guys seen anything like this?