Acronym | ... |
Name |
s-2N-x-2-x-M-o, M-prism-alternated 4N-gon - M-gon duoprism |
Circumradius | ... |
Face vector | 2nm, 4nm, 2nm+2n+m, 2n+m |
Especially | s4x2x3o (N=2, M=3) |
Confer |
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These isogonal polychora are obtained by M-prism alternation of the uniform 4N,M-duoprism (with N > 1, M > 2).
As mere alternations these come out to be nothing but 2N,M-duoprism variants. In fact, they then are yNx xMo with y=x(4N,3). Accordingly those obviously well could be resized to all unit edge lengths generally.
Incidence matrix according to Dynkin symbol
s2Nx2xMo (N>1, M>2) demi( . . . . ) | 2nm | 1 2 1 | 2 1 1 2 | 1 2 1 -----------------+-----+-----------+------------+------ demi( . x . . ) | 2 | nm * * | 2 0 1 0 | 1 2 0 demi( . . x . ) | 2 | * 2nm * | 1 1 0 1 | 1 1 1 sefa( s2Nx . . ) | 2 | * * nm | 0 0 1 2 | 0 2 1 y = x(4N,3) -----------------+-----+-----------+------------+------ demi( . x x . ) | 4 | 2 2 0 | nm * * * | 1 1 0 demi( . . xMo ) | m | 0 m 0 | * 2n * * | 1 0 1 s2Nx . . | 2n | n 0 n | * * m * | 0 2 0 xNy sefa( s2Nx2x . ) | 4 | 0 2 2 | * * * nm | 0 1 1 x2y -----------------+-----+-----------+------------+------ demi( . x xMo ) | 2m | m 2m 0 | m 2 0 0 | n * * M-p (uniform) s2Nx2x . | 4n | 2n 2n 2n | n 0 2 n | * m * 2N-p variant xNy x sefa( s2Nx2xMo ) | 2m | 0 2m m | 0 2 0 m | * * n M-p variant xMo y starting figure: x2Nx xMo
yNx xMo (N>1, M>2) where y = x(4N,3) . . . . | 2nm | 1 1 2 | 1 2 2 1 | 2 1 1 --------+-----+-----------+------------+------ y . . . | 2 | nm * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * nm * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 2nm | 0 1 1 1 | 1 1 1 --------+-----+-----------+------------+------ yNx . . | 2n | n n 0 | m * * * | 2 0 0 y . x . | 4 | 2 0 2 | * nm * * | 1 1 0 . x x . | 4 | 0 2 2 | * * nm * | 1 0 1 . . xMo | m | 0 0 m | * * * 2n | 0 1 1 --------+-----+-----------+------------+------ yNx x . | 4n | 2n 2n 2n | 2 n n 0 | m * * 2N-p variant y . xMo | 2m | m 0 2m | 0 m 0 2 | * n * M-p variant . x xMo | 2m | 0 m 2m | 0 0 m 2 | * * n M-p (uniform)
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