Convex polyhedron with five, six, or seven vertices at distinct corners of a cube
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What are the names of the convex polyhedron with five, six, or seven vertices, where all vertices lie at distinct corners of a cube? I'm particularly interested in the five vertex case.
geometry polyhedra
asked Dec 27 '11 at 15:40
SteveSteve
787
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$begingroup$
What are the names of the convex polyhedron with five, six, or seven vertices, where all vertices lie at distinct corners of a cube? I'm particularly interested in the five vertex case.
geometry polyhedra
asked Dec 27 '11 at 15:40
SteveSteve
787
$endgroup$
add a comment |
$begingroup$
What are the names of the convex polyhedron with five, six, or seven vertices, where all vertices lie at distinct corners of a cube? I'm particularly interested in the five vertex case.
geometry polyhedra
asked Dec 27 '11 at 15:40
SteveSteve
787
$endgroup$
What are the names of the convex polyhedron with five, six, or seven vertices, where all vertices lie at distinct corners of a cube? I'm particularly interested in the five vertex case.
geometry polyhedra
geometry polyhedra
asked Dec 27 '11 at 15:40
SteveSteve
787
asked Dec 27 '11 at 15:40
SteveSteve
787
edited Dec 27 '11 at 16:29
Steve
asked Dec 27 '11 at 15:40
SteveSteve
787
asked Dec 27 '11 at 15:40
SteveSteve
787
asked Dec 27 '11 at 15:40
SteveSteve
787
787
add a comment |
add a comment |
1 Answer
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$begingroup$
With five vertices, depending on which ones you choose, you can get an oblique square pyramid, an oblique rectangular pyramid, or an irregular triangular bipyramid with $S_3$ symmetry.
With six vertices, you can get a right isosceles triangular prism, an equilateral triangular right antiprism, or an irregular figure with $D_{2cdot 2}$ symmetry but no name that I know of.
I don't think the seven-vertex figure has any particular name.
Neither of these names are precise enough to express the fact that the vertices are chosen among the vertices of a cube.
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
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1 Answer
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1 Answer
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$begingroup$
With five vertices, depending on which ones you choose, you can get an oblique square pyramid, an oblique rectangular pyramid, or an irregular triangular bipyramid with $S_3$ symmetry.
With six vertices, you can get a right isosceles triangular prism, an equilateral triangular right antiprism, or an irregular figure with $D_{2cdot 2}$ symmetry but no name that I know of.
I don't think the seven-vertex figure has any particular name.
Neither of these names are precise enough to express the fact that the vertices are chosen among the vertices of a cube.
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
$endgroup$
add a comment |
$begingroup$
With five vertices, depending on which ones you choose, you can get an oblique square pyramid, an oblique rectangular pyramid, or an irregular triangular bipyramid with $S_3$ symmetry.
With six vertices, you can get a right isosceles triangular prism, an equilateral triangular right antiprism, or an irregular figure with $D_{2cdot 2}$ symmetry but no name that I know of.
I don't think the seven-vertex figure has any particular name.
Neither of these names are precise enough to express the fact that the vertices are chosen among the vertices of a cube.
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
$endgroup$
add a comment |
$begingroup$
With five vertices, depending on which ones you choose, you can get an oblique square pyramid, an oblique rectangular pyramid, or an irregular triangular bipyramid with $S_3$ symmetry.
With six vertices, you can get a right isosceles triangular prism, an equilateral triangular right antiprism, or an irregular figure with $D_{2cdot 2}$ symmetry but no name that I know of.
I don't think the seven-vertex figure has any particular name.
Neither of these names are precise enough to express the fact that the vertices are chosen among the vertices of a cube.
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
$endgroup$
With five vertices, depending on which ones you choose, you can get an oblique square pyramid, an oblique rectangular pyramid, or an irregular triangular bipyramid with $S_3$ symmetry.
With six vertices, you can get a right isosceles triangular prism, an equilateral triangular right antiprism, or an irregular figure with $D_{2cdot 2}$ symmetry but no name that I know of.
I don't think the seven-vertex figure has any particular name.
Neither of these names are precise enough to express the fact that the vertices are chosen among the vertices of a cube.
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
edited Dec 19 '18 at 14:15
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
answered Dec 27 '11 at 16:48
Henning MakholmHenning Makholm
241k17306544
241k17306544
add a comment |
add a comment |
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