Objects of constant width are well-known, and I have in my hand a (non-spherical) solid of constant diameter. The question arises:
Are there any non-spherical 3-dimensional objects such that their orthogonal projections are always the same area?
Most objects are such that as you turn them their shadow changes in area, but is this always the case, except for the sphere? This seems such an obvious question that I thought it must have been asked, and if asked, then either trivially answered, or well-known as an open question. However, moderate searches have failed to find any references.
Has anyone here studied this?
