s-n-s-2-s-2m-x,
edge-alternated 2n-gon - 4m-gon duoprism
- general polytopal classes:
- isogonal
links
, e.g.
(n = 3, m = 2)
(n = m = 3)
| Acronym | (n,2m)-pap |
| Name |
n-gon - 2m-gon prismantiprismoid, s-n-s-2-s-2m-x, edge-alternated 2n-gon - 4m-gon duoprism |
| Circumradius | ... |
| Face vector | 4nm, 12nm, 10nm+2n+4m, 2nm+2n+4m |
| Confer |
|
|
External links |
, e.g.
(n = 3, m = 2)
(n = m = 3)
|
These isogonal polychora are obtained by edge alternation of the uniform 2n,4m-duoprism (with n > 2, m > 1).
Conceptionally the dyad - 2m-gon prismantiprismoid (case n = 2) would belong here as well, but because of degeneracies the incidences then are slightly different and thus are provided in a different page.
Incidence matrix according to Dynkin symbol
s-n-s-2-s-2m-x (n > 2, m > 1)
demi( . . . . ) | 4nm | 1 1 1 2 1 | 1 1 3 2 2 2 | 1 1 1 1 3
-----------------------+-----+---------------------+-----------------------+--------------
demi( . . . x ) | 2 | 2nm * * * * | 0 1 0 2 1 1 | 0 1 1 1 2 x
s 2 s . | 2 | * 2nm * * * | 0 0 2 0 2 0 | 1 0 1 0 2 q
. s 2 s . | 2 | * * 2nm * * | 0 0 2 0 0 2 | 1 0 0 1 2 q
sefa( s-n-s . . ) | 2 | * * * 4nm * | 1 0 1 1 0 0 | 1 1 0 0 1 a=x(n,2)
sefa( . . s-2m-x ) | 2 | * * * * 2nm | 0 1 0 0 1 1 | 0 0 1 1 1 b=x(2m,3)
-----------------------+-----+---------------------+-----------------------+--------------
s-n-s . . | n | 0 0 0 n 0 | 4m * * * * * | 1 1 0 0 0 a-{n}
. . s-2m-x | 2m | m 0 0 0 m | * 2n * * * * | 0 0 1 1 0 (x,b)-{2m}
sefa( s-n-s-2-s . ) | 3 | 0 1 1 1 0 | * * 4nm * * * | 1 0 0 0 1 oa&#q
sefa( s-n-s 2 x ) | 4 | 2 0 0 2 0 | * * * 2nm * * | 0 1 0 0 1 (x,a)-{4}
sefa( s 2 s-2m-x ) | 4 | 1 2 0 0 1 | * * * * 2nm * | 0 0 1 0 1 xb&#q
sefa( . s-2-s-2m-x ) | 4 | 1 0 2 0 1 | * * * * * 2nm | 0 0 0 1 1 xb&#q
-----------------------+-----+---------------------+-----------------------+--------------
s-n-s-2-s . | 2n | 0 n n 2n 0 | 2 0 2n 0 0 0 | 2m * * * * ao-n-oa&#q, n-ap variant
s-n-s 2 x | 2n | n 0 0 2n 0 | 2 0 0 n 0 0 | * 2m * * * aa-n-oo&#x, n-p variant
s 2 s-2m-x | 4m | 2m 2m 0 0 2m | 0 2 0 0 2m 0 | * * n * * bx-m-xb&#q, trapezo-2m-p
. s-2-s-2m-x | 4m | 2m 0 2m 0 2m | 0 2 0 0 0 2m | * * * n * bx-m-xb&#q, trapezo-2m-p
sefa( s-n-s-2-s-2m-x ) | 6 | 2 2 2 2 1 | 0 0 2 1 1 1 | * * * * 2nm bx2oa&#q, wedge-like trip variant
starting figure: x-n-x x-2m-x
s-2n-o-2-s-2m-x (n > 2, m > 1)
demi( . . . . ) | 4nm | 1 2 2 1 | 1 1 3 2 4 | 1 1 2 3
------------------------+-----+-----------------+-------------------+-------------
demi( . . . x ) | 2 | 2nm * * * | 0 1 0 2 2 | 0 1 2 2 x
s 2 s . | 2 | * 4nm * * | 0 0 2 0 2 | 1 0 1 2 q
sefa( s-2n-o . . ) | 2 | * * 4nm * | 1 0 1 1 0 | 1 1 0 1 a=x(n,2)
sefa( . . s-2m-x ) | 2 | * * * 2nm | 0 1 0 0 2 | 0 0 2 1 b=x(2m,3)
------------------------+-----+-----------------+-------------------+-------------
s-2n-o . . | n | 0 0 n 0 | 4m * * * * | 1 1 0 0 a-{n}
. . s-2m-x | 2m | m 0 0 m | * 2n * * * | 0 0 2 0 (x,b)-{2m}
sefa( s-2n-o-2-s . ) | 3 | 0 2 1 0 | * * 4nm * * | 1 0 0 1 oa&#q
sefa( s-2n-o 2 x ) | 4 | 2 0 2 0 | * * * 2nm * | 0 1 0 1 (x,a)-{4}
sefa( s 2 s-2m-x ) | 4 | 1 2 0 1 | * * * * 4nm | 0 0 1 1 xb&#q
------------------------+-----+-----------------+-------------------+-------------
s-2n-o-2-s . | 2n | 0 2n 2n 0 | 2 0 2n 0 0 | 2m * * * ao-n-oa&#q, n-ap variant
s-2n-o 2 x | 2n | n 0 2n 0 | 2 0 0 n 0 | * 2m * * aa-n-oo&#x, n-p variant
s 2 s-2m-x | 4m | 2m 2m 0 2m | 0 2 0 0 2m | * * 2n * bx-m-xb&#q, trapezo-2m-p
sefa( s-2n-o-2-s-2m-x ) | 6 | 2 4 2 1 | 0 0 2 1 2 | * * * 2nm bx2oa&#q, wedge-like trip variant
starting figure: x-2n-o x-2m-x
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