Why is the number of veriticies different from the number of corners?

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http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/poincare_eng.html



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I count 20 corners but the site says it has 16 verticies. Is there a math word for "corner"?




geometry




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    The statement about "16 vertices" refers to the triangulation given in poincare.dat, not to the dodecahedron above.
    – Rahul
    Jul 22 at 5:51















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http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/poincare_eng.html



enter image description here



I count 20 corners but the site says it has 16 verticies. Is there a math word for "corner"?




geometry




share|cite|improve this question















  • 1




    The statement about "16 vertices" refers to the triangulation given in poincare.dat, not to the dodecahedron above.
    – Rahul
    Jul 22 at 5:51













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0
down vote

favorite









up vote
0
down vote

favorite











http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/poincare_eng.html



enter image description here



I count 20 corners but the site says it has 16 verticies. Is there a math word for "corner"?




geometry




share|cite|improve this question











http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/poincare_eng.html



enter image description here



I count 20 corners but the site says it has 16 verticies. Is there a math word for "corner"?





geometry





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asked Jul 22 at 5:31









Dale

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  • 1




    The statement about "16 vertices" refers to the triangulation given in poincare.dat, not to the dodecahedron above.
    – Rahul
    Jul 22 at 5:51













  • 1




    The statement about "16 vertices" refers to the triangulation given in poincare.dat, not to the dodecahedron above.
    – Rahul
    Jul 22 at 5:51








1




1




The statement about "16 vertices" refers to the triangulation given in poincare.dat, not to the dodecahedron above.
– Rahul
Jul 22 at 5:51





The statement about "16 vertices" refers to the triangulation given in poincare.dat, not to the dodecahedron above.
– Rahul
Jul 22 at 5:51











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The dodecahedron indeed has 20 vertices. But that's not what the sentence you refer to is counting.



Gluing opposite faces of the together (which requires considerable amounts of high-dimensional bending) turns that dodecahedron into the Poincaré homology sphere. And the resulting manifold can then be triangulated again using 16 vertices, with the combinatorics of the triangulation given in the file poincare.dat.






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    up vote
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    The dodecahedron indeed has 20 vertices. But that's not what the sentence you refer to is counting.



    Gluing opposite faces of the together (which requires considerable amounts of high-dimensional bending) turns that dodecahedron into the Poincaré homology sphere. And the resulting manifold can then be triangulated again using 16 vertices, with the combinatorics of the triangulation given in the file poincare.dat.






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      up vote
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      The dodecahedron indeed has 20 vertices. But that's not what the sentence you refer to is counting.



      Gluing opposite faces of the together (which requires considerable amounts of high-dimensional bending) turns that dodecahedron into the Poincaré homology sphere. And the resulting manifold can then be triangulated again using 16 vertices, with the combinatorics of the triangulation given in the file poincare.dat.






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        up vote
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        down vote









        The dodecahedron indeed has 20 vertices. But that's not what the sentence you refer to is counting.



        Gluing opposite faces of the together (which requires considerable amounts of high-dimensional bending) turns that dodecahedron into the Poincaré homology sphere. And the resulting manifold can then be triangulated again using 16 vertices, with the combinatorics of the triangulation given in the file poincare.dat.






        share|cite|improve this answer













        The dodecahedron indeed has 20 vertices. But that's not what the sentence you refer to is counting.



        Gluing opposite faces of the together (which requires considerable amounts of high-dimensional bending) turns that dodecahedron into the Poincaré homology sphere. And the resulting manifold can then be triangulated again using 16 vertices, with the combinatorics of the triangulation given in the file poincare.dat.







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        answered Jul 23 at 9:21









        MvG

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