These solids of constant width behave like spheres. This is because, regardless of the peculiar shape, the diameter is still equal at every point. You can demonstrate this property by setting a flat object, like a book, on them and it will roll as smoothly as if the object were on spheres. Additionally, these wonky shapes won't roll away.
The precise shape is an orbiform based on the revolution of a Reuleaux triangle.
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More info (from Wikipedia):
The Reuleaux tetrahedron is the intersection of four balls of radius centered at the vertices of a regular tetrahedron with side lengths. The spherical surface of the ball centered on each vertex passes through the other three vertices, which also form vertices of the Reuleaux tetrahedron. Thus the center of each ball is on the surfaces of the other three balls. The Reuleaux tetrahedron has the same face structure as a regular tetrahedron, but with curved faces: four vertices, and four curved faces, connected by six circular-arc edges.
This shape is defined and named by analogy to the Reuleaux triangle, a two-dimensional curve of constant width; both shapes are named after Franz Reuleaux, a 19th-century German engineer who did pioneering work on ways that machines translate one type of motion into another. One can find repeated claims in the mathematical literature that the Reuleaux tetrahedron is analogously a surface of constant width, but it is not true: the two midpoints of opposite edge arcs are separated by a larger distance.