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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

214.0. "Solid" by HARE::STAN () Thu Jan 24 1985 01:25

I am thinking of a solid figure with 6 faces, 8 vertices, and 12 edges.
There are 3 edges meeting at each vertex.
What is it?
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214.1MANANA::COLGATEThu Jan 24 1985 10:001
how about a cube.
214.2HARE::STANThu Jan 24 1985 12:343
[good straight man]

No, that's not what I'm thinking of.
214.3SPRITE::OSMANThu Jan 24 1985 12:352
Well then, how about NOT the cube, i.e. a solid object consisting of
the REST of the universe !
214.4METOO::YARBROUGHThu Jan 24 1985 12:536
No, Stan said nothing about its being regular. How about a 3-dimensional
hexalateral simplaex

(ARGGH!!)   simplex?

Lynn Yarbrough
214.5METOO::YARBROUGHThu Jan 24 1985 12:562
No, Yarbrough, that fits a hexahedron as well. Hmm. Well, how about a
hexahedral quadrilateral simplex?
214.6HARE::STANThu Jan 24 1985 17:032
re: 3 - Nah. Not the one I'm thinking of either.  The one I'm thinking
	of is simple, convex, closed and bounded.
214.7SPRITE::OSMANThu Jan 24 1985 17:185
How about something boring like a four-sided pyramid with the point
shaved off, i.e. a cubish object whose top is smaller than the bottom.

I know, I know, it matches but it's "not the one I'm thinking of" right ?

214.8TURTLE::GILBERTThu Jan 24 1985 19:098
re .-1
	Nah, that would be topologically equivalent to a cube, and would imply
	a poorly posed problem.

I've made the ridiculous assuptions that: this is a bounded object in 3-space,
and no face shares an edge with itself; and am still ready to give up.  Almost.

Perhaps there's a hole in the object, instead of my reasoning.
214.9HARE::STANThu Jan 24 1985 23:265
Peter is correct, I'm not thinking of the truncated pyramid with square base
or a rectangular solid.

The object I am thinking about has its faces meeting each other only
at edges.  It has no holes in it.  It lives in ordinary Euclidean 3-space.
214.10LATOUR::AMARTINFri Jan 25 1985 09:053
I'll say "rectangular prism", and hope that in this case that "rectangular"
does not force any edges to be the same length.  Or "trapezial prism"?
				/AHM
214.11METOO::YARBROUGHFri Jan 25 1985 09:282
AHA! It's a triangular pyramid with two corners truncated.
Lynn Yarbrough
214.12HARE::STANFri Jan 25 1985 12:401
Sorry, I'm not thinking of a rectangular prism.
214.13HARE::STANFri Jan 25 1985 12:411
Sorry, I'm not thinking of a trapezial prism either.
214.14HARE::STANFri Jan 25 1985 12:447
Re: 11 - A winner. (Lynn)

Yes, I was thinking of a tetrahedron with two corners truncated.

The resulting solid has 6 faces, 2 of them are pentagons, 2 of them
are quadrilaterals and 2 of them are triangles.  The two pentagons
share a common edge, as do the two quadrilaterals.
214.15SPRITE::OSMANMon Jan 28 1985 15:235
I don't understand the answer.  A picture is worth a thousand words.  Please
draw it.

Thanks !

214.16R2ME2::GILBERTTue Jan 29 1985 02:243
Pyramix is a Rubik's Cube-like puzzle, in the shape of a tetrahedron (a pyramid
with a three-sided base).  Break or cut off two of the (four) corners.  Can you
picture it now?
214.17METOO::YARBROUGHTue Jan 29 1985 10:2814
Here 'tis. The dotted horizontal line does not intersect the solid lines.
                _______
               / \   / \
              /   \ /   \
             /     |     \
            /      |      \
           /       |       \
          /........|........\
          \        |        /
           \       |       /
            \      |      /
             \    / \    /
              \  /   \  /
               \/_____\/