perplexus.info :: Geometry : Cutting Cubic Corners

Cutting Cubic Corners (Posted on 2005-07-27)

Take a perfect cube. While keeping the cube intact and all the pieces together, make as many planar slices as possible through exactly three vertices.

After doing so, separate the resulting pieces. What shapes result and how many are there of each and in total?

To what do these numbers correspond?

Note: Please do NOT punch the problem into a 3D graphics program and then rush to post the solution here so you can be first. This remains my most enjoyable solution to date because I attempted it without pen and paper, computer or polyhedron.

Submitted by Charley

Rating: 4.5000 (2 votes)

Solution: (Hide)

21 pieces total.
From a regular cube with edge length of 1:
12 irregular tetrahedrons with edge lengths of 1, sqrt(2)/2, sqrt(2)/2, sqrt(2)/2, sqrt(2)/2, and sqrt(2)/2. (one for each cube edge)
8 regular tetrahedrons with edge length sqrt(2)/2. (one for each vertex)
1 regular octahedrons with edge length sqrt(2)/2. (one for the center of the cube)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Remembr-do it in yr head	Percy	2005-08-19 13:56:52
Can't miss this one	Tristan	2005-08-10 04:39:15
re: Pencil and Paper used ...	Josh70679	2005-07-27 22:10:36
Pencil and Paper used ...	Charlie	2005-07-27 20:42:16
guess	Josh70679	2005-07-27 20:34:59

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info