Acronym n-cufbil
Name n-gonal cupofastegia biluna
Lace city
in approx. ASCII-art
   xNo  
        
xNo  xNx
        
   xNo  
Especially tritep (n=2)*   tracufbil (n=3)   squacufbil (n=4)*  
Confer
related segmentochora:
n-cuf  
general polytopal classes:
bistratic lace towers  

* The case n=2 equally would be considerable here by concept, it just has a different incidence matrix as the n-gons become degenerate. Further their tets would become corealmic and thus combine to trits. – Conversely, the other extreme at n=4 makes the n-cupolas corealmic, so that the two remaining squacues combine there into a single squobcu. – Outside that intervall these polychora won't be CRFs any longer.


Incidence matrix according to Dynkin symbol

x(xx)x-n-o(ox)o&#xt   → height = ???
({n} || pseudo n-cu || {n})

o(..).-n-o(..).    | n *  * * | 2 1  2 0  0 0 0 0  0 0 | 1 2 2 1  2 0 0 0 0  0 0 0 0 0 | 1 1 2 1 0 0 0 0
.(o.).-n-.(o.).    | * n  * * | 0 1  0 2  2 1 0 0  0 0 | 0 2 0 0  2 1 2 1 2  2 0 0 0 0 | 1 0 2 1 1 2 1 0
.(.o).-n-.(.o).    | * * 2n * | 0 0  1 0  1 0 1 1  1 0 | 0 0 1 1  1 0 1 1 0  1 1 1 1 0 | 0 1 1 1 0 1 1 1
.(..)o-n-.(..)o    | * *  * n | 0 0  0 0  0 1 0 0  2 2 | 0 0 0 0  0 0 0 0 2  2 0 2 1 1 | 0 0 0 0 1 2 1 1
-------------------+----------+------------------------+-------------------------------+----------------
x(..).   .(..).    | 2 0  0 0 | n *  * *  * * * *  * * | 1 1 1 0  0 0 0 0 0  0 0 0 0 0 | 1 1 1 0 0 0 0 0
o(o.).-n-o(o.).&#x | 1 1  0 0 | * n  * *  * * * *  * * | 0 2 0 0  2 0 0 0 0  0 0 0 0 0 | 1 0 2 1 0 0 0 0
o(.o).-n-o(.o).&#x | 1 0  1 0 | * * 2n *  * * * *  * * | 0 0 1 1  1 0 0 0 0  0 0 0 0 0 | 0 1 1 1 0 0 0 0
.(x.).   .(..).    | 0 2  0 0 | * *  * n  * * * *  * * | 0 1 0 0  0 1 1 0 1  0 0 0 0 0 | 1 0 1 0 1 1 0 0
.(oo).-n-.(oo).&#x | 0 1  1 0 | * *  * * 2n * * *  * * | 0 0 0 0  1 0 1 1 0  1 0 0 0 0 | 0 0 1 1 0 1 1 0
.(o.)o-n-.(o.)o&#x | 0 1  0 1 | * *  * *  * n * *  * * | 0 0 0 0  0 0 0 0 2  2 0 0 0 0 | 0 0 0 0 1 2 1 0
.(.x).   .(..).    | 0 0  2 0 | * *  * *  * * n *  * * | 0 0 1 0  0 0 1 0 0  0 1 1 0 0 | 0 1 1 0 0 1 0 1
.(..).   .(.x).    | 0 0  2 0 | * *  * *  * * * n  * * | 0 0 0 1  0 0 0 1 0  0 1 0 1 0 | 0 1 0 1 0 0 1 1
.(.o)o-n-.(.o)o&#x | 0 0  1 1 | * *  * *  * * * * 2n * | 0 0 0 0  0 0 0 0 0  1 0 1 1 0 | 0 0 0 0 0 1 1 1
.(..)x   .(..).    | 0 0  0 2 | * *  * *  * * * *  * n | 0 0 0 0  0 0 0 0 1  0 0 1 0 1 | 0 0 0 0 1 1 0 1
-------------------+----------+------------------------+-------------------------------+----------------
x(..).-n-o(..).    | n 0  0 0 | n 0  0 0  0 0 0 0  0 0 | 1 * * *  * * * * *  * * * * * | 1 1 0 0 0 0 0 0
x(x.).   .(..).&#x | 2 2  0 0 | 1 2  0 1  0 0 0 0  0 0 | * n * *  * * * * *  * * * * * | 1 0 1 0 0 0 0 0
x(.x).   .(..).&#x | 2 0  2 0 | 1 0  2 0  0 0 1 0  0 0 | * * n *  * * * * *  * * * * * | 0 1 1 0 0 0 0 0
.(..).   o(.x).&#x | 1 0  2 0 | 0 0  2 0  0 0 0 1  0 0 | * * * n  * * * * *  * * * * * | 0 1 0 1 0 0 0 0
o(oo).-n-o(oo).&#x | 1 1  1 0 | 0 1  1 0  1 0 0 0  0 0 | * * * * 2n * * * *  * * * * * | 0 0 1 1 0 0 0 0
.(x.).-n-.(o.).    | 0 n  0 0 | 0 0  0 n  0 0 0 0  0 0 | * * * *  * 1 * * *  * * * * * | 1 0 0 0 1 0 0 0
.(xx).   .(..).&#x | 0 2  2 0 | 0 0  0 1  2 0 1 0  0 0 | * * * *  * * n * *  * * * * * | 0 0 1 0 0 1 0 0
.(..).   .(ox).&#x | 0 1  2 0 | 0 0  0 0  2 0 0 1  0 0 | * * * *  * * * n *  * * * * * | 0 0 0 1 0 0 1 0
.(x.)x   .(..).&#x | 0 2  0 2 | 0 0  0 1  0 2 0 0  0 1 | * * * *  * * * * n  * * * * * | 0 0 0 0 1 1 0 0
.(oo)o-n-.(oo)o&#x | 0 1  1 1 | 0 0  0 0  1 1 0 0  1 0 | * * * *  * * * * * 2n * * * * | 0 0 0 0 0 1 1 0
.(.x).-n-.(.x).    | 0 0 2n 0 | 0 0  0 0  0 0 n n  0 0 | * * * *  * * * * *  * 1 * * * | 0 1 0 0 0 0 0 1
.(.x)x   .(..).&#x | 0 0  2 2 | 0 0  0 0  0 0 1 0  2 1 | * * * *  * * * * *  * * n * * | 0 0 0 0 0 1 0 1
.(..).   .(.x)o&#x | 0 0  2 1 | 0 0  0 0  0 0 0 1  2 0 | * * * *  * * * * *  * * * n * | 0 0 0 0 0 0 1 1
.(..)x-n-.(..)o    | 0 0  0 n | 0 0  0 0  0 0 0 0  0 n | * * * *  * * * * *  * * * * 1 | 0 0 0 0 1 0 0 1
-------------------+----------+------------------------+-------------------------------+----------------
x(x.).-n-o(o.).&#x  n n  0 0 | n n  0 n  0 0 0 0  0 0 | 1 n 0 0  0 1 0 0 0  0 0 0 0 0 | 1 * * * * * * *
x(.x).-n-o(.x).&#x  n 0 2n 0 | n 0 2n 0  0 0 n n  0 0 | 1 0 n n  0 0 0 0 0  0 1 0 0 0 | * 1 * * * * * *
x(xx).   .(..).&#x  2 2  2 0 | 1 2  2 1  2 0 1 0  0 0 | 0 1 1 0  2 0 1 0 0  0 0 0 0 0 | * * n * * * * *
.(..).   o(ox).&#x  1 1  2 0 | 0 1  2 0  2 0 0 1  0 0 | 0 0 0 1  2 0 0 1 0  0 0 0 0 0 | * * * n * * * *
.(x.)x-n-.(o.)o&#x  0 n  0 n | 0 0  0 n  0 n 0 0  0 n | 0 0 0 0  0 1 0 0 n  0 0 0 0 1 | * * * * 1 * * *
.(xx)x   .(..).&#x  0 2  2 2 | 0 0  0 1  2 2 1 0  2 1 | 0 0 0 0  0 0 1 0 1  2 0 1 0 0 | * * * * * n * *
.(..).   .(ox)o&#x  0 1  2 1 | 0 0  0 0  2 1 0 1  2 0 | 0 0 0 0  0 0 0 1 0  2 0 0 1 0 | * * * * * * n *
.(.x)x-n-.(.x)o&#x  0 0 2n n | 0 0  0 0  0 0 n n 2n n | 0 0 0 0  0 0 0 0 0  0 1 n n 1 | * * * * * * * 1
or
o(..).-n-o(..).     & | 2n *  * |  2  1  2 0  0 0 0 | 1  2  2  1  2 0 0 0 0 | 1 1  2  1
.(o.).-n-.(o.).       |  * n  * |  0  2  0 2  2 0 0 | 0  4  0  0  4 1 2 1 0 | 2 0  4  2
.(.o).-n-.(.o).       |  * * 2n |  0  0  2 0  1 1 1 | 0  0  2  2  2 0 1 1 1 | 0 2  2  2
----------------------+---------+-------------------+-----------------------+----------
x(..).   .(..).     & |  2 0  0 | 2n  *  * *  * * * | 1  1  1  0  0 0 0 0 0 | 1 1  1  0
o(o.).-n-o(o.).&#x  & |  1 1  0 |  * 2n  * *  * * * | 0  2  0  0  2 0 0 0 0 | 1 0  2  1
o(.o).-n-o(.o).&#x  & |  1 0  1 |  *  * 4n *  * * * | 0  0  1  1  1 0 0 0 0 | 0 1  1  1
.(x.).   .(..).       |  0 2  0 |  *  *  * n  * * * | 0  2  0  0  0 1 1 0 0 | 2 0  2  0
.(oo).-n-.(oo).&#x    |  0 1  1 |  *  *  * * 2n * * | 0  0  0  0  2 0 1 1 0 | 0 0  2  2
.(.x).   .(..).       |  0 0  2 |  *  *  * *  * n * | 0  0  2  0  0 0 1 0 1 | 0 2  2  0
.(..).   .(.x).       |  0 0  2 |  *  *  * *  * * n | 0  0  0  2  0 0 0 1 1 | 0 2  0  2
----------------------+---------+-------------------+-----------------------+----------
x(..).-n-o(..).     & |  n 0  0 |  n  0  0 0  0 0 0 | 2  *  *  *  * * * * * | 1 1  0  0
x(x.).   .(..).&#x  & |  2 2  0 |  1  2  0 1  0 0 0 | * 2n  *  *  * * * * * | 1 0  1  0
x(.x).   .(..).&#x  & |  2 0  2 |  1  0  2 0  0 1 0 | *  * 2n  *  * * * * * | 0 1  1  0
.(..).   o(.x).&#x  & |  1 0  2 |  0  0  2 0  0 0 1 | *  *  * 2n  * * * * * | 0 1  0  1
o(oo).-n-o(oo).&#x  & |  1 1  1 |  0  1  1 0  1 0 0 | *  *  *  * 4n * * * * | 0 0  1  1
.(x.).-n-.(o.).       |  0 n  0 |  0  0  0 n  0 0 0 | *  *  *  *  * 1 * * * | 2 0  0  0
.(xx).   .(..).&#x    |  0 2  2 |  0  0  0 1  2 1 0 | *  *  *  *  * * n * * | 0 0  2  0
.(..).   .(ox).&#x    |  0 1  2 |  0  0  0 0  2 0 1 | *  *  *  *  * * * n * | 0 0  0  2
.(.x).-n-.(.x).       |  0 0 2n |  0  0  0 0  0 n n | *  *  *  *  * * * * 1 | 0 2  0  0
----------------------+---------+-------------------+-----------------------+----------
x(x.).-n-o(o.).&#x  &   n n  0 |  n  n  0 n  0 0 0 | 1  n  0  0  0 1 0 0 0 | 2 *  *  *
x(.x).-n-o(.x).&#x  &   n 0 2n |  n  0 2n 0  0 n n | 1  0  n  n  0 0 0 0 1 | * 2  *  *
x(xx).   .(..).&#x  &   2 2  2 |  1  2  2 1  2 1 0 | 0  1  1  0  2 0 1 0 0 | * * 2n  *
.(..).   o(ox).&#x  &   1 1  2 |  0  1  2 0  2 0 1 | 0  0  0  1  2 0 0 1 0 | * *  * 2n

© 2004-2018
top of page