Acronym | n-cufbil |
Name | n-gonal cupofastegia biluna |
Lace city in approx. ASCII-art |
xNo xNo xNx xNo |
Face vector | 5n, 13n, 12n+4, 4n+4 |
Especially | tritep (n=2)* tracufbil (n=3) squacufbil (n=4)* |
Confer |
|
* 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
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