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Take a cube and imagine a plane slicing through that cube. As that plane is tilted at different angles and positioned in different places, what will be the possible intersection of the plane and the cube look like? What planar shapes can you obtain as cross sections?

2007-04-26 05:19:35 · 3 answers · asked by heythere 2 in Science & Mathematics Mathematics

3 answers

Of the planar shapes or cross-sections possible: 3,4,5 and 6 p-gons. Regular p-gons are possible with all but the pentagon (Scythian’s question). I constructed a pentagon using midpoints along the edges of a hexahedron, noting 4 equal sides and a long side (base) with 2 right angles.
(looks like a house)

http://en.wikipedia.org/wiki/Cube
http://mathworld.wolfram.com/Cube.html

P.S. If you're interested in pentagons you might note that one of 14 known types of convex pentagons that tessellate also has 4 equal sides and 2 right angles, however, none of those sides are parallel as they must be in the cases above.

http://www.mathpuzzle.com/tilepent.html
http://burtleburtle.net/bob/tile/pentagon.html
http://britton.disted.camosun.bc.ca/jbperplex.htm

For info on cubes with MORE than three dimensions...
http://en.wikipedia.org/wiki/Tesseract

...DON'T ask about slicing those.

2007-04-27 09:16:56 · answer #1 · answered by JJ 2 · 1 0

This Site Might Help You.

RE:
Slicing a cube... planar sections?
Take a cube and imagine a plane slicing through that cube. As that plane is tilted at different angles and positioned in different places, what will be the possible intersection of the plane and the cube look like? What planar shapes can you obtain as cross sections?

2015-08-13 02:32:47 · answer #2 · answered by Anonymous · 0 0

if you make a vertical cut, the resulting planar shape will be a square since the cubes has all equal sides

At an angle from the vertical, the resulting planar surface will be a rectangle since the vertical legs will be longer than the horizontal legs.

if the slice is made at more complex angles, i.e. tilted and rotated, you can get rectangles of varying side lengths

If the slice is tilted and rotated, you can get trapezoids with the top and bottom sides at different lengths with different sloping sides.

If you cut from the corner, you can get triangles as well.

2007-04-26 05:38:48 · answer #3 · answered by minorchord2000 6 · 0 0

The cube has 6 faces, so the maximum number of sides a polygon cross-section can have is 6. In fact, polygon cross-sections of 3, 4, 5, and 6 sides are possible. Of those, regular polygons of 3, 4, and 6 sides are possible. The one interesting question here is whether or not a regular pentagon cross-section is possible. So, that will be my next question posted.

2007-04-26 05:58:35 · answer #4 · answered by Scythian1950 7 · 2 0

3 planes will divide the cube in to 2 cuboids

4 planes will divide the cube in to 2 prisms

4 planes will divide the cube in to 2 pyramids

2007-04-26 05:38:56 · answer #5 · answered by MinazZ 2 · 0 0

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