It looks like there are two places on the wiki page that mention these conditions. The first is at the top of the page, and includes the self-dual condition: In fact, the 24-cell is the unique convex self-dual regular Euclidean polytope in [sic] which is neither a polygon nor a simplex. The second, which Fred quoted, is further down on the page and omits this condition: The 24-cell is the unique convex regular Euclidean polytope that is neither a polygon nor a simplex. Relaxing the condition of convexity admits two further figures: the great 120-cell and grand stellated 120-cell Apparently this page could use some work. Tom Adam P. Goucher writes:
Self-dual.
Sent: Monday, March 09, 2015 at 1:36 AM From: "Fred Lunnon" <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] 24-cell --- it sez 'ere ...
At https://en.wikipedia.org/wiki/24-cell we are informed that
<< The 24-cell is the unique convex regular Euclidean polytope that is neither a polygon nor a simplex. Relaxing the condition of convexity admits two further figures: the great 120-cell and grand stellated 120-cell >>
The first sentence is plainly false as it stands (eg. octahedron, tesseract); the second (sic: missing period) yields me no clue as to what might instead have been intended by the first.
Any ideas out there?
WFL