Question

If sides of a cube are cut, what are the number of faces and vertices of the new polyhedron?

Answer 1

The extent of the cut is not defined. Thus there are 2 answers.

See explanation

Explanation:

`color( purple)("General comment")`

In the question you use the word 'sides'. I took this to mean the equivalent of 'sides of a square'. The proper name for this is edges.

The other possibility is that you meant 'surface'. My solution has been edited and changed by Shwetank who took it to mean (corners) vertices.

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`color(blue)("Cut as Cube A")`

Note that I have not shown all corners as cut. They are!

The cube before cutting has `12` edges

After cutting it has `8` additional triangles at `3` sides each so the final count is:

`12+(8xx3)=36`

Number of vertices are `3xx8=24` and faces are `6+8=14`

`color(blue)("Cut as Cube B")`

`6` blue faces each having `4` edges giving

`6xx4=24`

Number of vertices are `12` and faces are `6+8=14`