Besides a circle, is there any other shape that can rotate within a triangle?

If I were to have a square, it is obvious that a circle can rotate within it, which means that the circle can make a 360° rotation inside of the square while always touching the four sides of the square. There are, however, other shapes that can do this, such as the Reuleaux triangle. These shapes are called curves of constant width. Each one of this shapes, dispite being non-circular, can rotate within a square without losing contact on any of the sides.

My question involves an equilateral triangle instead of a square. It is also clear that a circle can rotate within an equilateral triangle without losing contact on any sides, but are there any other shapes that can do this?