We're used to drawing 2D projections of 3D shapes. This process can be extended to n-dimensions by defining a 2D direction for each of the n coordinate axes. Modifying these 2D directions gives a different perspective on the nD shape. This example shows the result for various shapes including the unit simplex, unit cube, and unit sphere.
"Depth" is the dimension(s) that are lost in the 2D projection. For an n-dimensional shape, depth is n-2 dimensional. When drawing a 3D shape, depth is 1-dimensional, ie. there is a line of points (coming towards the camera) that are indistinguishable in the picture. When drawing a 4D shape, depth is 2-dimensional, ie. there is a plane of points (in the 4D space) that are indistinguishable. When drawing a 5D shape, depth is 3-dimensional...
We can't fully "see" n-dimensions, but we can see 2D or 3D subspaces of the nD space. The question then becomes can we trick our brains into stitching those 2D/3D subspaces back together into some "nD" image. The answer remains unclear.