It cannot be a polygon since they must have the same number of sides and angles. It cannot be a solid object because the Euler characteristic would require it to have 0 faces!

Leonhard Euler

The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.

Lucie Euler's birth name is Lucie Luise Euler.

Leonhard Euler (after whom it was named).

Leonhard Euler (after whom it was named).

Leonhard Euler (after whom it was named).

Leonhard Euler (after whom it was named).