What is the term to use for 1-dimensional polytope?
$begingroup$
I am assuming that a polygon is defined as a 2-dimensional polytope.
In that case, a 1-dimensional polytope will be a connected union of line segments. In other words, it is a physical realization of a graph.
Is there a short professional term for this concept?
geometry polytopes
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
asked Dec 22 '18 at 20:26
yigoliyigoli
177
$endgroup$
add a comment |
$begingroup$
I am assuming that a polygon is defined as a 2-dimensional polytope.
In that case, a 1-dimensional polytope will be a connected union of line segments. In other words, it is a physical realization of a graph.
Is there a short professional term for this concept?
geometry polytopes
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
asked Dec 22 '18 at 20:26
yigoliyigoli
177
$endgroup$
$begingroup$
A chain of segments and a $1$-complex come to mind, depending on your set-up. Why not use "an embedding of a connected graph"?
$endgroup$
– Michael Burr
Dec 22 '18 at 20:29
1
$begingroup$
Guy Inchbald suggests Polytelon, Ditelon, Dion, or Dyad
$endgroup$
– Henry
Dec 22 '18 at 20:32
1
$begingroup$
Polytelon sounds nice and proper. Who is Guy Inchbald? I think there is not a consensus for this concept yet?
$endgroup$
– yigoli
Dec 22 '18 at 20:41
$begingroup$
@elasolova amazon.co.uk/Books-Guy-Inchbald/….
$endgroup$
– Paul Frost
Dec 23 '18 at 0:15
add a comment |
$begingroup$
I am assuming that a polygon is defined as a 2-dimensional polytope.
In that case, a 1-dimensional polytope will be a connected union of line segments. In other words, it is a physical realization of a graph.
Is there a short professional term for this concept?
geometry polytopes
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
asked Dec 22 '18 at 20:26
yigoliyigoli
177
$endgroup$
I am assuming that a polygon is defined as a 2-dimensional polytope.
In that case, a 1-dimensional polytope will be a connected union of line segments. In other words, it is a physical realization of a graph.
Is there a short professional term for this concept?
geometry polytopes
geometry polytopes
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
asked Dec 22 '18 at 20:26
yigoliyigoli
177
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
asked Dec 22 '18 at 20:26
yigoliyigoli
177
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
edited Dec 22 '18 at 20:40
Viktor Glombik
1,0121528
1,0121528
asked Dec 22 '18 at 20:26
yigoliyigoli
177
asked Dec 22 '18 at 20:26
yigoliyigoli
177
asked Dec 22 '18 at 20:26
yigoliyigoli
177
177
$begingroup$
A chain of segments and a $1$-complex come to mind, depending on your set-up. Why not use "an embedding of a connected graph"?
$endgroup$
– Michael Burr
Dec 22 '18 at 20:29
1
$begingroup$
Guy Inchbald suggests Polytelon, Ditelon, Dion, or Dyad
$endgroup$
– Henry
Dec 22 '18 at 20:32
1
$begingroup$
Polytelon sounds nice and proper. Who is Guy Inchbald? I think there is not a consensus for this concept yet?
$endgroup$
– yigoli
Dec 22 '18 at 20:41
$begingroup$
@elasolova amazon.co.uk/Books-Guy-Inchbald/….
$endgroup$
– Paul Frost
Dec 23 '18 at 0:15
add a comment |
$begingroup$
A chain of segments and a $1$-complex come to mind, depending on your set-up. Why not use "an embedding of a connected graph"?
$endgroup$
– Michael Burr
Dec 22 '18 at 20:29
1
$begingroup$
Guy Inchbald suggests Polytelon, Ditelon, Dion, or Dyad
$endgroup$
– Henry
Dec 22 '18 at 20:32
1
$begingroup$
Polytelon sounds nice and proper. Who is Guy Inchbald? I think there is not a consensus for this concept yet?
$endgroup$
– yigoli
Dec 22 '18 at 20:41
$begingroup$
@elasolova amazon.co.uk/Books-Guy-Inchbald/….
$endgroup$
– Paul Frost
Dec 23 '18 at 0:15
$begingroup$
A chain of segments and a $1$-complex come to mind, depending on your set-up. Why not use "an embedding of a connected graph"?
$endgroup$
– Michael Burr
Dec 22 '18 at 20:29
$begingroup$
A chain of segments and a $1$-complex come to mind, depending on your set-up. Why not use "an embedding of a connected graph"?
$endgroup$
– Michael Burr
Dec 22 '18 at 20:29
1
1
$begingroup$
Guy Inchbald suggests Polytelon, Ditelon, Dion, or Dyad
$endgroup$
– Henry
Dec 22 '18 at 20:32
$begingroup$
Guy Inchbald suggests Polytelon, Ditelon, Dion, or Dyad
$endgroup$
– Henry
Dec 22 '18 at 20:32
1
1
$begingroup$
Polytelon sounds nice and proper. Who is Guy Inchbald? I think there is not a consensus for this concept yet?
$endgroup$
– yigoli
Dec 22 '18 at 20:41
$begingroup$
Polytelon sounds nice and proper. Who is Guy Inchbald? I think there is not a consensus for this concept yet?
$endgroup$
– yigoli
Dec 22 '18 at 20:41
$begingroup$
@elasolova amazon.co.uk/Books-Guy-Inchbald/….
$endgroup$
– Paul Frost
Dec 23 '18 at 0:15
$begingroup$
@elasolova amazon.co.uk/Books-Guy-Inchbald/….
$endgroup$
– Paul Frost
Dec 23 '18 at 0:15
add a comment |
1 Answer
1
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$begingroup$
I am Guy Inchbald.
In modern polytope theory, a 1-dimensional polytope is just a single closed line segment, meaning the end points are included as its vertices. A full-blown graph is effectively a polyhedron, as it has the same combinatorial structure (Search for Grünbaum on "Polyhedra as graphs, graphs as polyhedra").
There is indeed no consensus yet on what to call the 1-polytope. Amazingly, the first time that any term was formally used was not until 2018, in Prof. Norman Johnson's "Geometries and Transformations" (Cambridge University Press). He used "dion". This was some years after a few people had used "dyad" informally, which I thought unsuitable because it was used for other things and also begged the question, two of what? So I had proposed "ditelon". Johnson contracted it "dion" for his book, which I also find unsuitable because it begs the same question. A "ditelon" it a two-ended thing, "telos" being the end of say a rope, in the same way that a polygon has "many corners" and a polyhedron has "many seats" or faces. You know what you are talking about.
Who am I? Nobody very much, I have just published a few papers on polyhedra. You can find a fuller explanation of the issue on my web site at http://www.steelpillow.com/polyhedra/ditela.html
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
$endgroup$
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
add a comment |
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1 Answer
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$begingroup$
I am Guy Inchbald.
In modern polytope theory, a 1-dimensional polytope is just a single closed line segment, meaning the end points are included as its vertices. A full-blown graph is effectively a polyhedron, as it has the same combinatorial structure (Search for Grünbaum on "Polyhedra as graphs, graphs as polyhedra").
There is indeed no consensus yet on what to call the 1-polytope. Amazingly, the first time that any term was formally used was not until 2018, in Prof. Norman Johnson's "Geometries and Transformations" (Cambridge University Press). He used "dion". This was some years after a few people had used "dyad" informally, which I thought unsuitable because it was used for other things and also begged the question, two of what? So I had proposed "ditelon". Johnson contracted it "dion" for his book, which I also find unsuitable because it begs the same question. A "ditelon" it a two-ended thing, "telos" being the end of say a rope, in the same way that a polygon has "many corners" and a polyhedron has "many seats" or faces. You know what you are talking about.
Who am I? Nobody very much, I have just published a few papers on polyhedra. You can find a fuller explanation of the issue on my web site at http://www.steelpillow.com/polyhedra/ditela.html
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
$endgroup$
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
add a comment |
$begingroup$
I am Guy Inchbald.
In modern polytope theory, a 1-dimensional polytope is just a single closed line segment, meaning the end points are included as its vertices. A full-blown graph is effectively a polyhedron, as it has the same combinatorial structure (Search for Grünbaum on "Polyhedra as graphs, graphs as polyhedra").
There is indeed no consensus yet on what to call the 1-polytope. Amazingly, the first time that any term was formally used was not until 2018, in Prof. Norman Johnson's "Geometries and Transformations" (Cambridge University Press). He used "dion". This was some years after a few people had used "dyad" informally, which I thought unsuitable because it was used for other things and also begged the question, two of what? So I had proposed "ditelon". Johnson contracted it "dion" for his book, which I also find unsuitable because it begs the same question. A "ditelon" it a two-ended thing, "telos" being the end of say a rope, in the same way that a polygon has "many corners" and a polyhedron has "many seats" or faces. You know what you are talking about.
Who am I? Nobody very much, I have just published a few papers on polyhedra. You can find a fuller explanation of the issue on my web site at http://www.steelpillow.com/polyhedra/ditela.html
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
$endgroup$
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
add a comment |
$begingroup$
I am Guy Inchbald.
In modern polytope theory, a 1-dimensional polytope is just a single closed line segment, meaning the end points are included as its vertices. A full-blown graph is effectively a polyhedron, as it has the same combinatorial structure (Search for Grünbaum on "Polyhedra as graphs, graphs as polyhedra").
There is indeed no consensus yet on what to call the 1-polytope. Amazingly, the first time that any term was formally used was not until 2018, in Prof. Norman Johnson's "Geometries and Transformations" (Cambridge University Press). He used "dion". This was some years after a few people had used "dyad" informally, which I thought unsuitable because it was used for other things and also begged the question, two of what? So I had proposed "ditelon". Johnson contracted it "dion" for his book, which I also find unsuitable because it begs the same question. A "ditelon" it a two-ended thing, "telos" being the end of say a rope, in the same way that a polygon has "many corners" and a polyhedron has "many seats" or faces. You know what you are talking about.
Who am I? Nobody very much, I have just published a few papers on polyhedra. You can find a fuller explanation of the issue on my web site at http://www.steelpillow.com/polyhedra/ditela.html
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
$endgroup$
I am Guy Inchbald.
In modern polytope theory, a 1-dimensional polytope is just a single closed line segment, meaning the end points are included as its vertices. A full-blown graph is effectively a polyhedron, as it has the same combinatorial structure (Search for Grünbaum on "Polyhedra as graphs, graphs as polyhedra").
There is indeed no consensus yet on what to call the 1-polytope. Amazingly, the first time that any term was formally used was not until 2018, in Prof. Norman Johnson's "Geometries and Transformations" (Cambridge University Press). He used "dion". This was some years after a few people had used "dyad" informally, which I thought unsuitable because it was used for other things and also begged the question, two of what? So I had proposed "ditelon". Johnson contracted it "dion" for his book, which I also find unsuitable because it begs the same question. A "ditelon" it a two-ended thing, "telos" being the end of say a rope, in the same way that a polygon has "many corners" and a polyhedron has "many seats" or faces. You know what you are talking about.
Who am I? Nobody very much, I have just published a few papers on polyhedra. You can find a fuller explanation of the issue on my web site at http://www.steelpillow.com/polyhedra/ditela.html
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
answered Jan 11 at 18:38
Guy InchbaldGuy Inchbald
111
111
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
add a comment |
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
$begingroup$
But I always thought that a single closed line segment is the 1-dimensional simplex. A triangle being 2-dimensional simplex. A connected composition of triangles and lesser dimensional simplexes(i.e. line segments) being a 2-dimensional polytope. By the same analogy, can't we say a connected composition of closed line-segments is a 1-dimensional polytope? I think I need to do some more research. Thanks for caring to answer my question.
$endgroup$
– yigoli
Jan 12 at 19:10
add a comment |
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$begingroup$
A chain of segments and a $1$-complex come to mind, depending on your set-up. Why not use "an embedding of a connected graph"?
$endgroup$
– Michael Burr
Dec 22 '18 at 20:29
1
$begingroup$
Guy Inchbald suggests Polytelon, Ditelon, Dion, or Dyad
$endgroup$
– Henry
Dec 22 '18 at 20:32
1
$begingroup$
Polytelon sounds nice and proper. Who is Guy Inchbald? I think there is not a consensus for this concept yet?
$endgroup$
– yigoli
Dec 22 '18 at 20:41
$begingroup$
@elasolova amazon.co.uk/Books-Guy-Inchbald/….
$endgroup$
– Paul Frost
Dec 23 '18 at 0:15