[math-fun] Simplest planar n-gon polyhedra
At https://math.stackexchange.com/questions/2869725/ I've started a sequence. What is the fewest number of planar but possibly irregular n-gons needed to make a polyhedron or toroid? 4 triangles 6 squares 12 pentagons 7 hexagons 12 heptagons Correct so far? How many octagons are needed? Ed Pegg Jr
Are you requiring that the polygons all be congruent? On 2018-08-02 11:53, Ed Pegg Jr wrote:
At https://math.stackexchange.com/questions/2869725/ I've started a sequence. What is the fewest number of planar but possibly irregular n-gons needed to make a polyhedron or toroid?
4 triangles 6 squares 12 pentagons 7 hexagons 12 heptagons
Correct so far? How many octagons are needed?
Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Conguent, no. Just planar. On Thu, Aug 2, 2018 at 2:21 PM William R Somsky <wrsomsky@gmail.com> wrote:
Are you requiring that the polygons all be congruent?
On 2018-08-02 11:53, Ed Pegg Jr wrote:
At https://math.stackexchange.com/questions/2869725/ I've started a sequence. What is the fewest number of planar but possibly irregular n-gons needed to make a polyhedron or toroid?
4 triangles 6 squares 12 pentagons 7 hexagons 12 heptagons
Correct so far? How many octagons are needed?
Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I toyed with the idea of removing a few cubies from a 3x3x3 cube so that each of the 12 planes would include an octagonal face. Perhaps there is a simple argument as to why this wouldn't work.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Ed Pegg Jr Sent: Thursday, August 02, 2018 3:25 PM To: math-fun Subject: Re: [math-fun] Simplest planar n-gon polyhedra
Conguent, no. Just planar.
On Thu, Aug 2, 2018 at 2:21 PM William R Somsky <wrsomsky@gmail.com> wrote:
Are you requiring that the polygons all be congruent?
On 2018-08-02 11:53, Ed Pegg Jr wrote:
At https://math.stackexchange.com/questions/2869725/ I've started a sequence. What is the fewest number of planar but possibly irregular n-gons needed to make a polyhedron or toroid?
4 triangles 6 squares 12 pentagons 7 hexagons 12 heptagons
Correct so far? How many octagons are needed?
Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Andrew Weimholt discussed related questions at Quora: Does-a-polyhedron-exist-in-which-all-faces-are-octagons <https://www.quora.com/Does-a-polyhedron-exist-in-which-all-faces-are-octagons> How-many-faces-would-a-polytope-consisting-of-octagonal-faces-have-if-only-three-faces-meet-at-each-vertex-Does-it-have-a-name <https://www.quora.com/How-many-faces-would-a-polytope-consisting-of-octagonal-faces-have-if-only-three-faces-meet-at-each-vertex-Does-it-have-a-name> On Thu, Aug 2, 2018 at 2:53 PM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
At https://math.stackexchange.com/questions/2869725/ I've started a sequence. What is the fewest number of planar but possibly irregular n-gons needed to make a polyhedron or toroid?
4 triangles 6 squares 12 pentagons 7 hexagons 12 heptagons
Correct so far? How many octagons are needed?
Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
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David Wilson -
Ed Pegg Jr -
W. Edwin Clark -
William R Somsky