naraht wrote:sorry, meant 24 choron for each half.
It appears that to create an anti-prism in n-space, you must start with a polytope in dimension n-1 that is its own dual, so you have the 3-space antiprisms, the anti-prisms formed from n-1 simplexes (where the anti-prism is the n-orthoplexes) and then this beast.
What is it's preferred name?
Mercurial, the Spectre wrote:We are into a debate on what antiprisms are.
Klitzing wrote:Mercurial, the Spectre wrote:We are into a debate on what antiprisms are.
Indeed!
Once again, Mercurial is refering more to the second part of the term "antiprism", so suggestively asking for 2 identical bases, whereas I refer to the first part of that term "antiprism", which clearly refers to duality. The prism part here then just refers to the stacking operation. (Just as Wendy's term of "laceprisms" herewith only refers to that stacking operation.)
His argument wrt. 4D duoantiprisms is not valid, as there again we are back to 2D polygons, where the gyration and the duality come out to be the same.
Also he was reading my paragraph on gyroprisms wrong. Gyroprisms indeed are stacks - or more generally simplices of mutually gyrated (or obtionally reflected for n=2). Thus the refered 6D candidate is clearly there called a "gyrotrigonism", e.g. hexgyt = tedjak = xoo3ooo3oxo *b3oox&#x , whereas hin indeed is a hexgyp = xo3oo3ox *b3oo&#x.
Infact there is no predefined "geometrical fact" which relates the term "antiprism" to snubs (alternations). It just happens within 3D to fall together. But this is just because of gyroprisms are related to alternations (generally).
Btw. Mercurial's description of the icoap as a true alternation (this time derived from a prism of some Catalan hypersolid) indeed is correct. But obviously he is cheating here, as he applies snubbing only onto a dual of the appropriate compound.
I also agree in the isogonality, but wrt. gyroprisms (and gyrosimplices). Antiprisms (within my usage of the term), i.e. stacks of dual polytopes, only become isogonal if the base happens to be selfdual (like all 2D polygons). So e.g. hex = tet || dual tet is isogonal, but octap = oct || cube and ikap = ike || doe are not.
--- rk
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