A Regular Hendecachoron

This is a hendecachoron by Carlo Séquin.

The hendecachoron “(11-cell) is a regular self-dual 4-dimensional polytope composed from eleven non-orientable, self-intersecting hemi-icosahedra. This intriguing object of high combinatorial symmetry was discovered in 1976 by Branko Grünbaum and later rediscovered and analyzed from a group rheoretic point of view by H.S.M. Coxeter.”

That’s what he wrote in his paper, Hyperseeing the Regular Hendecachoron.

Now, if you’re a layman like me, you’d probably not get a single word out of the statement I blatantly copied and pasted from his paper. But simply put, here’s what it is - it’s a 4 dimensional geometry. A polychoron is in 4D as what a polygon is in 2D. Many 4 dimensional objects are self intersecting (think Klein bottles), so yeah, you can think of a hendecachoron as a geometrical shape on 4 dimensional space.

The picture above is a hendecachoron that has been ‘ruled’. A typical hendecachoron looks thusly (also courtesy of Prof. Séquin):