Acronym | n-cuf |
Name |
n-gonal cupofastegium, 2n-gon - n-prismatic wedge, n-gonal orthobicupolaic ring, {2n} || n-prism, {n} || n-cupola |
Segmentochoron display | |
Circumradius | sqrt[(5+2 cos(π/n)-4cos2(π/n))/(8-12 cos2(π/n))] |
Lace city in approx. ASCII-art |
x-n-x x-n-o x-n-o |
Face vector | 4n, 9n, 7n+3, 2n+3 |
Especially | {4} || ortho {4} (n=2)* {6} || trip (n=3) {8} || cube (n=4) {10} || pip (n=5) |
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.
Incidence matrix according to Dynkin symbol
xx-n-ox xo&#x (2 < n < 5.104299) → height = sqrt[3 - 1/sin2(π/n)]/2
(n-p || {2n})
o.-n-o. o. | 2n * | 2 1 2 0 0 | 1 2 2 1 2 0 | 1 1 2 1
.o-n-.o .o | * 2n | 0 0 2 1 1 | 0 0 2 2 1 1 | 0 2 1 1
--------------+-------+-------------+----------------+--------
x. .. .. | 2 0 | 2n * * * * | 1 1 1 0 0 0 | 1 1 1 0
.. .. x. | 2 0 | * n * * * | 0 2 0 0 2 0 | 1 0 2 1
oo-n-oo oo&#x | 1 1 | * * 4n * * | 0 0 1 1 1 0 | 0 1 1 1
.x .. .. | 0 2 | * * * n * | 0 0 2 0 0 1 | 0 2 1 0
.. .x .. | 0 2 | * * * * n | 0 0 0 2 0 1 | 0 2 0 1
--------------+-------+-------------+----------------+--------
x.-n-o. .. | n 0 | n 0 0 0 0 | 2 * * * * * | 1 1 0 0
x. .. x. | 4 0 | 2 2 0 0 0 | * n * * * * | 1 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 2n * * * | 0 1 1 0
.. ox ..&#x | 1 2 | 0 0 2 0 1 | * * * 2n * * | 0 1 0 1
.. .. xo&#x | 2 1 | 0 1 2 0 0 | * * * * 2n * | 0 0 1 1
.x-n-.x .. | 0 2n | 0 0 0 n n | * * * * * 1 | 0 2 0 0
--------------+-------+-------------+----------------+--------
x.-n-o. x. ♦ 2n 0 | 2n n 0 0 0 | 2 n 0 0 0 0 | 1 * * *
xx-n-ox ..&#x ♦ n 2n | n 0 2n n n | 1 0 n n 0 1 | * 2 * *
xx .. xo&#x ♦ 4 2 | 2 2 4 1 0 | 0 1 2 0 2 0 | * * n *
.. ox xo&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 0 2 2 0 | * * * n
xxx-n-oxo&#x → height(1,2) = height(2,3) = sqrt[4 - 1/sin2(π/n)]/2 height(1,3) = 1 o..-n-o.. | n * * | 2 2 1 0 0 0 0 | 1 2 1 2 2 0 0 0 0 | 1 1 2 1 0 .o.-n-.o. | * 2n * | 0 1 0 1 1 1 0 | 0 1 1 0 1 1 1 1 0 | 1 0 1 1 1 ..o-n-..o | * * n | 0 0 1 0 0 2 2 | 0 0 0 2 2 0 2 1 1 | 0 1 2 1 1 -------------+--------+-----------------+--------------------+---------- x.. ... | 2 0 0 | n * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0 oo.-n-oo.&#x | 1 1 0 | * 2n * * * * * | 0 1 1 0 1 0 0 0 0 | 1 0 1 1 0 o.o-n-o.o&#x | 1 0 1 | * * n * * * * | 0 0 0 2 2 0 0 0 0 | 0 1 2 1 0 .x. ... | 0 2 0 | * * * n * * * | 0 1 0 0 0 1 1 0 0 | 1 0 1 0 1 ... .x. | 0 2 0 | * * * * n * * | 0 0 1 0 0 1 0 1 0 | 1 0 0 1 1 .oo-n-.oo | 0 1 1 | * * * * * 2n * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 ..x ... | 0 0 2 | * * * * * * n | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1 -------------+--------+-----------------+--------------------+---------- x..-n-o.. | n 0 0 | n 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0 xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * n * * * * * * * | 1 0 1 0 0 ... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * n * * * * * * | 1 0 0 1 0 x.x ...&#x | 2 0 2 | 1 0 2 0 0 0 1 | * * * n * * * * * | 0 1 1 0 0 ooo-n-ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * 2n * * * * | 0 0 1 1 0 .x.-n-.x. | 0 2n 0 | 0 0 0 n n 0 0 | * * * * * 1 * * * | 1 0 0 0 1 .xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 | * * * * * * n * * | 0 0 1 0 1 ... .xo&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * n * | 0 0 0 1 1 ..x-n-..o | 0 0 n | 0 0 0 0 0 0 n | * * * * * * * * 1 | 0 1 0 0 1 -------------+--------+-----------------+--------------------+---------- xx.-n-ox.&#x ♦ n 2n 0 | n 2n 0 n n 0 0 | 1 n n 0 0 1 0 0 0 | 1 * * * * x.x-n-o.o&#x ♦ n 0 n | n 0 n 0 0 0 n | 1 0 0 n 0 0 0 0 1 | * 1 * * * xxx ...&#x ♦ 2 2 2 | 1 2 2 1 0 2 1 | 0 1 0 1 2 0 1 0 0 | * * n * * ... oxo&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 | 0 0 1 0 2 0 0 1 0 | * * * n * .xx-n-.oo&#x ♦ 0 2n n | 0 0 0 n n 2n n | 0 0 0 0 0 1 n n 1 | * * * * 1
or o..-n-o.. & | 2n * | 2 2 1 0 0 | 1 2 1 2 2 0 | 1 1 2 1 .o.-n-.o. | * 2n | 0 2 0 1 1 | 0 2 2 0 1 1 | 2 0 1 1 ----------------+-------+-------------+----------------+-------- x.. ... & | 2 0 | 2n * * * * | 1 1 0 1 0 0 | 1 1 1 0 oo.-n-oo.&#x & | 1 1 | * 4n * * * | 0 1 1 0 1 0 | 1 0 1 1 o.o-n-o.o&#x | 2 0 | * * n * * | 0 0 0 2 2 0 | 0 1 2 1 .x. ... | 0 2 | * * * n * | 0 2 0 0 0 1 | 2 0 1 0 ... .x. | 0 2 | * * * * n | 0 0 2 0 0 1 | 2 0 0 1 ----------------+-------+-------------+----------------+-------- x..-n-o.. & | n 0 | n 0 0 0 0 | 2 * * * * * | 1 1 0 0 xx. ...&#x & | 2 2 | 1 2 0 1 0 | * 2n * * * * | 1 0 1 0 ... ox.&#x & | 1 2 | 0 2 0 0 1 | * * 2n * * * | 1 0 0 1 x.x ...&#x | 4 0 | 2 0 2 0 0 | * * * n * * | 0 1 1 0 ooo-n-ooo&#x | 2 1 | 0 2 1 0 0 | * * * * 2n * | 0 0 1 1 .x.-n-.x. | 0 2n | 0 0 0 n n | * * * * * 1 | 2 0 0 0 ----------------+-------+-------------+----------------+-------- xx.-n-ox.&#x & ♦ n 2n | n 2n 0 n n | 1 n n 0 0 1 | 2 * * * x.x-n-o.o&#x ♦ 2n 0 | 2n 0 n 0 0 | 2 0 0 n 0 0 | * 1 * * xxx ...&#x ♦ 4 2 | 2 4 2 1 0 | 0 2 0 1 2 0 | * * n * ... oxo&#x ♦ 2 2 | 0 4 1 0 1 | 0 0 2 0 2 0 | * * * n
{n} || n-cu → height = ???
o..-n-o.. | n * * | 2 2 1 0 0 0 0 | 1 2 1 2 2 0 0 0 0 | 1 1 2 1 0
.o.-n-.o. | * 2n * | 0 1 0 1 1 1 0 | 0 1 1 0 1 1 1 1 0 | 1 0 1 1 1
..o-n-..o | * * n | 0 0 1 0 0 2 2 | 0 0 0 2 2 0 2 1 1 | 0 1 2 1 1
-------------+--------+-----------------+--------------------+----------
x.. ... | 2 0 0 | n * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.-n-oo.&#x | 1 1 0 | * 2n * * * * * | 0 1 1 0 1 0 0 0 0 | 1 0 1 1 0
o.o-n-o.o&#x | 1 0 1 | * * n * * * * | 0 0 0 2 2 0 0 0 0 | 0 1 2 1 0
.x. ... | 0 2 0 | * * * n * * * | 0 1 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x. | 0 2 0 | * * * * n * * | 0 0 1 0 0 1 0 1 0 | 1 0 0 1 1
.oo-n-.oo | 0 1 1 | * * * * * 2n * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ... | 0 0 2 | * * * * * * n | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
-------------+--------+-----------------+--------------------+----------
x..-n-o.. | n 0 0 | n 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * n * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * n * * * * * * | 1 0 0 1 0
x.x ...&#x | 2 0 2 | 1 0 2 0 0 0 1 | * * * n * * * * * | 0 1 1 0 0
ooo-n-ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * 2n * * * * | 0 0 1 1 0
.x.-n-.x. | 0 2n 0 | 0 0 0 n n 0 0 | * * * * * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 | * * * * * * n * * | 0 0 1 0 1
... .xo&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * n * | 0 0 0 1 1
..x-n-..o | 0 0 n | 0 0 0 0 0 0 n | * * * * * * * * 1 | 0 1 0 0 1
-------------+--------+-----------------+--------------------+----------
xx.-n-ox.&#x ♦ n 2n 0 | n 2n 0 n n 0 0 | 1 n n 0 0 1 0 0 0 | 1 * * * *
x.x-n-o.o&#x ♦ n 0 n | n 0 n 0 0 0 n | 1 0 0 n 0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2 2 2 | 1 2 2 1 0 2 1 | 0 1 0 1 2 0 1 0 0 | * * n * *
... oxo&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 | 0 0 1 0 2 0 0 1 0 | * * * n *
.xx-n-.oo&#x ♦ 0 2n n | 0 0 0 n n 2n n | 0 0 0 0 0 1 n n 1 | * * * * 1
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