| Acronym | ..., N-g || N-appip |
| Name |
N-gon atop N-appip, (N-gon, N-p, gyro N-p)-trigonic |
| Circumradius | ... |
|
Lace city in approx. ASCII-art |
o oNx
x oNx x xNo
|
| Face vector | 5n, 17n, 21n+5, 11n+8, 2n+5 |
| Especially | taope (N=3) |
| Confer |
|
For non-convex cases use N = n/d.
Incidence matrix according to Dynkin symbol
xxoNoox oxx &#x → height(1,2) = sqrt(3)/2 = 0.866025
height(1,3) = sqrt[(1+3 cos(π/N))/(4+4 cos(π/N))]
height(2,3) = sqrt[(1+2 cos(π/N))/(2+2 cos(π/N))]
o..No.. o.. | n * * | 2 2 4 0 0 0 0 0 | 1 4 1 4 2 2 4 0 0 0 0 0 0 0 | 2 2 2 2 1 4 2 2 0 0 0 0 0 | 1 1 2 2 1 0
.o.N.o. .o. | * 2n * | 0 1 0 2 1 2 0 0 | 0 2 1 0 0 0 2 1 2 2 1 2 0 0 | 1 2 0 0 0 2 1 2 1 1 2 1 0 | 1 0 1 2 1 1
..oN..o ..o | * * 2n | 0 0 2 0 0 2 2 1 | 0 0 0 1 2 2 2 0 0 1 2 2 1 2 | 0 0 1 1 2 1 2 2 0 1 1 2 1 | 0 1 1 1 2 1
----------------+---------+----------------------+-------------------------------------+------------------------------+------------
x.. ... ... | 2 0 0 | n * * * * * * * | 1 2 0 2 0 0 0 0 0 0 0 0 0 0 | 2 1 2 1 0 2 0 0 0 0 0 0 0 | 1 1 2 1 0 0
oo.Noo. oo. &#x | 1 1 0 | * 2n * * * * * * | 0 2 1 0 0 0 2 0 0 0 0 0 0 0 | 1 2 0 0 0 2 1 2 0 0 0 0 0 | 1 0 1 2 1 0
o.oNo.o o.o &#x | 1 0 1 | * * 4n * * * * * | 0 0 0 1 1 1 1 0 0 0 0 0 0 0 | 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x. ... ... | 0 2 0 | * * * 2n * * * * | 0 1 0 0 0 0 0 1 1 1 0 0 0 0 | 1 1 0 0 0 1 0 0 1 1 1 0 0 | 1 0 1 1 0 1
... ... .x. | 0 2 0 | * * * * n * * * | 0 0 1 0 0 0 0 0 2 0 0 2 0 0 | 0 2 0 0 0 0 0 2 1 0 2 1 0 | 1 0 0 2 1 1
.ooN.oo .oo &#x | 0 1 1 | * * * * * 4n * * | 0 0 0 0 0 0 1 0 0 1 1 1 0 0 | 0 0 0 0 0 1 1 1 0 1 1 1 0 | 0 0 1 1 1 1
... ..x ... | 0 0 2 | * * * * * * 2n * | 0 0 0 0 1 0 0 0 0 0 1 0 1 1 | 0 0 1 0 1 0 1 0 0 1 0 1 1 | 0 1 1 0 1 1
... ... ..x | 0 0 2 | * * * * * * * n | 0 0 0 0 0 2 0 0 0 0 0 2 0 2 | 0 0 0 1 2 0 0 2 0 0 1 2 1 | 0 1 0 1 2 1
----------------+---------+----------------------+-------------------------------------+------------------------------+------------
x..No.. ... | n 0 0 | n 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
xx. ... ... &#x | 2 2 0 | 1 2 0 1 0 0 0 0 | * 2n * * * * * * * * * * * * | 1 1 0 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
... ... ox. &#x | 1 2 0 | 0 2 0 0 1 0 0 0 | * * n * * * * * * * * * * * | 0 2 0 0 0 0 0 2 0 0 0 0 0 | 1 0 0 2 1 0
x.o ... ... &#x | 2 0 1 | 1 0 2 0 0 0 0 0 | * * * 2n * * * * * * * * * * | 0 0 1 1 0 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
... o.x ... &#x | 1 0 2 | 0 0 2 0 0 0 1 0 | * * * * 2n * * * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... ... o.x &#x | 1 0 2 | 0 0 2 0 0 0 0 1 | * * * * * 2n * * * * * * * * | 0 0 0 1 1 0 0 1 0 0 0 0 0 | 0 1 0 1 1 0
oooNooo ooo &#x | 1 1 1 | 0 1 1 0 0 1 0 0 | * * * * * * 4n * * * * * * * | 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x.N.o. ... | 0 n 0 | 0 0 0 n 0 0 0 0 | * * * * * * * 2 * * * * * * | 1 0 0 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1
.x. ... .x. | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * * * * * n * * * * * | 0 1 0 0 0 0 0 0 1 0 1 0 0 | 1 0 0 1 0 1
.xo ... ... &#x | 0 2 1 | 0 0 0 1 0 2 0 0 | * * * * * * * * * 2n * * * * | 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 1 1 0 1
... .ox ... &#x | 0 1 2 | 0 0 0 0 0 2 1 0 | * * * * * * * * * * 2n * * * | 0 0 0 0 0 0 1 0 0 1 0 1 0 | 0 0 1 0 1 1
... ... .xx &#x | 0 2 2 | 0 0 0 0 1 2 0 1 | * * * * * * * * * * * 2n * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 1
..oN..x ... | 0 0 n | 0 0 0 0 0 0 n 0 | * * * * * * * * * * * * 2 * | 0 0 1 0 0 0 0 0 0 1 0 0 1 | 0 1 1 0 0 1
... ..x ..x | 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * n | 0 0 0 0 1 0 0 0 0 0 0 1 1 | 0 1 0 0 1 1
----------------+---------+----------------------+-------------------------------------+------------------------------+------------
xx.Noo. ... &#x ♦ n n 0 | n n 0 n 0 0 0 0 | 1 n 0 0 0 0 0 1 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 1 0 1 0 0 0
xx. ... ox. &#x ♦ 2 4 0 | 1 4 0 2 2 0 0 0 | 0 2 2 0 0 0 0 0 1 0 0 0 0 0 | * n * * * * * * * * * * * | 1 0 0 1 0 0
x.oNo.x ... &#x ♦ n 0 n | n 0 2n 0 0 0 n 0 | 1 0 0 n n 0 0 0 0 0 0 0 1 0 | * * 2 * * * * * * * * * * | 0 1 1 0 0 0
x.o ... o.x &#x ♦ 2 0 2 | 1 0 4 0 0 0 0 1 | 0 0 0 2 0 2 0 0 0 0 0 0 0 0 | * * * n * * * * * * * * * | 0 1 0 1 0 0
... o.x o.x &#x ♦ 1 0 4 | 0 0 4 0 0 0 2 2 | 0 0 0 0 2 2 0 0 0 0 0 0 0 1 | * * * * n * * * * * * * * | 0 1 0 0 1 0
xxo ... ... &#x ♦ 2 2 1 | 1 2 2 1 0 2 0 0 | 0 1 0 1 0 0 2 0 0 1 0 0 0 0 | * * * * * 2n * * * * * * * | 0 0 1 1 0 0
... oox ... &#x ♦ 1 1 2 | 0 1 2 0 0 2 1 0 | 0 0 0 0 1 0 2 0 0 0 1 0 0 0 | * * * * * * 2n * * * * * * | 0 0 1 0 1 0
... ... oxx &#x ♦ 1 2 2 | 0 2 2 0 1 2 0 1 | 0 0 1 0 0 1 2 0 0 0 0 1 0 0 | * * * * * * * 2n * * * * * | 0 0 0 1 1 0
.x.N.o. .x. ♦ 0 2n 0 | 0 0 0 2n n 0 0 0 | 0 0 0 0 0 0 0 2 n 0 0 0 0 0 | * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xoN.ox ... &#x ♦ 0 n n | 0 0 0 n 0 2n n 0 | 0 0 0 0 0 0 0 1 0 n n 0 1 0 | * * * * * * * * * 2 * * * | 0 0 1 0 0 1
.xo ... .xx &#x ♦ 0 4 2 | 0 0 0 2 2 4 0 1 | 0 0 0 0 0 0 0 0 1 2 0 2 0 0 | * * * * * * * * * * n * * | 0 0 0 1 0 1
... .ox .xx &#x ♦ 0 2 4 | 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 2 2 0 1 | * * * * * * * * * * * n * | 0 0 0 0 1 1
..oN..x ..x ♦ 0 0 2n | 0 0 0 0 0 0 2n n | 0 0 0 0 0 0 0 0 0 0 0 0 2 n | * * * * * * * * * * * * 1 | 0 1 0 0 0 1
----------------+---------+----------------------+-------------------------------------+------------------------------+------------
xx.Noo. ox. &#x ♦ n 2n 0 | n 2n 0 2n n 0 0 0 | 1 2n n 0 0 0 0 2 n 0 0 0 0 0 | 2 n 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
x.oNo.x o.x &#x ♦ n 0 2n | n 0 4n 0 0 0 2n n | 1 0 0 2n 2n 2n 0 0 0 0 0 0 2 n | 0 0 2 n n 0 0 0 0 0 0 0 1 | * 1 * * * *
xxoNoox ... &#x ♦ n n n | n n 2n n 0 2n n 0 | 1 n 0 n n 0 2n 1 0 n n 0 1 0 | 1 0 1 0 0 n n 0 0 1 0 0 0 | * * 2 * * *
xxo ... oxx &#x ♦ 2 4 2 | 1 4 4 2 2 4 0 1 | 0 2 2 2 0 2 4 0 1 2 0 2 0 0 | 0 1 0 1 0 2 0 2 0 0 1 0 0 | * * * n * *
... oox oxx &#x ♦ 1 2 4 | 0 2 4 0 1 4 2 2 | 0 0 1 0 2 2 4 0 0 0 2 2 0 1 | 0 0 0 0 1 0 2 2 0 0 0 1 0 | * * * * n *
.xoN.ox .xx &#x ♦ 0 2n 2n | 0 0 0 2n n 4n 2n n | 0 0 0 0 0 0 0 2 n 2n 2n 2n 2 n | 0 0 0 0 0 0 0 0 1 2 n n 1 | * * * * * 1
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