Menger slicing

Geometry Level 3

How good are your visualization skills?

The above shape is called a menger sponge .

It's been sliced through the center by a plane perpendicular to the long diagonal.

What type of shape is left on the cross section?

  • Since this is a tier two menger sponge ( M 2 ) (M_2) there will be two different sizes of the same shape.
  • Do not consider the big hexagon on the outside, the one you get from slicing a regular cube. Just consider what shape is on the inside of the hexagon.
Triangle Hexagon None of the other answers Square 4-point star 6-point star

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4 solutions

Isaac Buckley
Jul 15, 2015

Here it is!

menger2 menger2

Nice problem :)

Jessica Wang - 5 years, 11 months ago

How could you?

Adam Phúc Nguyễn - 5 years, 9 months ago
Sue Harris
Jul 24, 2015

Apparently, my visualization skills were challenged on this one. I needed help. I used LegoDigitalDesigner to create some Menger Sponges.

Here are M1, M2, M3, and M4:

Then I cutaway the designated half revealing the star at the middle, highlighted here in a different color.

Michael Mendrin
Jul 15, 2015

Okay, I have to admit, that was unexpected.

Adams Ayoade
Dec 15, 2018

Woah! Nice visualization problem.

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