What solid object can fill 3 different geometrical shape one after the next, without reforming the shape?

Question

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Ok, there is a block of wood here is an example:
-------------------
| _ |
| /_\ |_| O |
|__________ |

/_\=triangle
|_|= Square
O=circle

the shapes are carved into the wood all the way through (like a prism through the wood, with the base shape on each end)

here is a side view with x ray vision!

_____________

|||||||||||||||||||||||||||||||||||||||
_____________

the |||||'s are hollow

Answer 1

This is an old puzzle that was popular way back when. Martin Gardner among others described it. You can start with a cork. Cut it crosswise so it's as long as it is wide. This will fit the circle in one direction and the square in another. Now cut a slice that goes from a diameter line of the circle at one end to a point on the very edge of the cork at the other end. Repeat, going from the same diameter to a point opposite the previous one. You now have a sort of wedge-shaped plug that fits a triangle whose base and altitude are equal, in addition to the square and the circle. The plug doesn't "fill" the tunnels you describe but it completely blocks them. I doubt you can make anything that fills all three tunnels.
The ref. provides a 3D animation of the plug. You need quicktime to run it.

Answer 2

Probably what you're thinking of:
An equilateral triangle. It will fit three shapes in the following way:

a) 1: by itself

b) 2: forming a regular rhombus

c) 6: forming a regular hexagon

Answer 3

A cube could be fit into a smaller pyramid, rectangle, or prism . . .

Answer 4

a aquare?