| Acronym | ... |
| Name |
{N} atop gyrated 3,N-dip, (N-g, dual N-g, N-p)-trigonic |
| Circumradius | ... |
|
Lace hyper city in approx. ASCII-art |
oNx
xNo
xNo
xNo
(shallow triangular pyramid with {N}-tip and all dual {N}'s for base vertices)
|
| Face vector | 4n, 13n, 16n+4, 9n+6, 2n+4 |
| Especially | trial triddip (N=3) |
| Confer |
|
For non-convex cases use N = n/d.
Incidence matrix according to Dynkin symbol
xoNox ox3oo&#x
({N} || gyro 3,N-dip)
o.No. o.3o. | n * | 2 6 0 0 | 1 6 3 6 0 0 0 | 3 6 3 2 0 0 | 3 2 1 0
.oN.o .o3.o | * 3n | 0 2 2 2 | 0 1 2 4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1
---------------+------+------------+-------------------+----------------+--------
x. .. .. .. | 2 0 | n * * * | 1 3 0 0 0 0 0 | 3 3 0 0 0 0 | 3 1 0 0
ooNoo oo3oo&#x | 1 1 | * 6n * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0
.. .x .. .. | 0 2 | * * 3n * | 0 0 1 0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1
.. .. .x .. | 0 2 | * * * 3n | 0 0 0 2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1
---------------+------+------------+-------------------+----------------+--------
x.No. .. .. | n 0 | n 0 0 0 | 1 * * * * * * | 3 0 0 0 0 0 | 3 0 0 0
xo .. .. ..&#x | 2 1 | 1 2 0 0 | * 3n * * * * * | 1 2 0 0 0 0 | 2 1 0 0
.. ox .. ..&#x | 1 2 | 0 2 1 0 | * * 3n * * * * | 1 0 2 0 0 0 | 2 0 1 0
.. .. ox ..&#x | 1 2 | 0 2 0 1 | * * * 6n * * * | 0 1 1 1 0 0 | 1 1 1 0
.oN.x .. .. | 0 n | 0 0 n 0 | * * * * 3 * * | 1 0 0 0 2 0 | 2 0 0 1
.. .x .x .. | 0 4 | 0 0 2 2 | * * * * * 3n * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x3.o | 0 3 | 0 0 0 3 | * * * * * * n | 0 0 0 2 0 2 | 0 1 2 1
---------------+------+------------+-------------------+----------------+--------
xoNox .. ..&#x ♦ n n | n 2n n 0 | 1 n n 0 1 0 0 | 3 * * * * * | 2 0 0 0
xo .. ox ..&#x ♦ 2 2 | 1 4 0 1 | 0 2 0 2 0 0 0 | * 3n * * * * | 1 1 0 0
.. ox ox ..&#x ♦ 1 4 | 0 4 2 2 | 0 0 2 2 0 1 0 | * * 3n * * * | 1 0 1 0
.. .. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 0 0 3 0 0 1 | * * * 2n * * | 0 1 1 0
.oN.x .x .. ♦ 0 2n | 0 0 2n n | 0 0 0 0 2 n 0 | * * * * 3 * | 1 0 0 1
.. .x .x3.o ♦ 0 6 | 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * n | 0 0 1 1
---------------+------+------------+-------------------+----------------+--------
xoNox ox ..&#x ♦ n 2n | n 4n 2n n | 1 2n 2n 2n 2 n 0 | 2 n n 0 1 0 | 3 * * *
xo .. ox3oo&#x ♦ 2 3 | 1 6 0 3 | 0 3 0 6 0 0 1 | 0 3 0 2 0 0 | * n * *
.. ox ox3oo&#x ♦ 1 6 | 0 6 3 6 | 0 0 3 6 0 3 2 | 0 0 3 2 0 1 | * * n *
.oN.x .x3.o ♦ 0 3n | 0 0 3n 3n | 0 0 0 0 3 3n n | 0 0 0 0 3 n | * * * 1
xxoNoox xoo&#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.. | 2n * * | 2 1 1 2 0 0 0 | 1 2 2 1 2 1 2 2 0 0 0 0 | 1 1 2 1 2 1 2 1 2 0 | 1 1 1 2 1
.o.N.o. .o. | * n * | 0 0 2 0 2 2 0 | 0 0 4 1 0 0 0 4 1 2 1 0 | 0 2 2 0 0 0 4 2 2 1 | 1 0 2 2 1
..oN..o ..o | * * n | 0 0 0 4 0 2 2 | 0 0 0 0 2 4 2 4 0 1 2 1 | 0 0 0 2 1 2 2 4 2 1 | 0 1 2 1 2
---------------+--------+-------------------+------------------------------+------------------------+----------
x.. ... ... | 2 0 0 | 2n * * * * * * | 1 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 1 1 0 1 0 0 0 | 1 1 1 1 0
... ... x.. | 2 0 0 | * n * * * * * | 0 2 0 1 0 0 2 0 0 0 0 0 | 1 0 2 0 2 1 0 0 2 0 | 1 1 0 2 1
oo.Noo. oo.&#x | 1 1 0 | * * 2n * * * * | 0 0 2 1 0 0 0 2 0 0 0 0 | 0 1 2 0 0 0 2 1 2 0 | 1 0 1 2 1
o.oNo.o o.o&#x | 1 0 1 | * * * 4n * * * | 0 0 0 0 1 1 1 1 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1
.x. ... ... | 0 2 0 | * * * * n * * | 0 0 2 0 0 0 0 0 1 1 0 0 | 0 2 1 0 0 0 2 0 0 1 | 1 0 2 1 0
.ooN.oo .oo&#x | 0 1 1 | * * * * * 2n * | 0 0 0 0 0 0 0 2 0 1 1 0 | 0 0 0 0 0 0 2 2 1 1 | 0 0 2 1 1
... ..x ... | 0 0 2 | * * * * * * n | 0 0 0 0 0 2 0 0 0 0 1 1 | 0 0 0 2 0 1 0 2 0 1 | 0 1 2 0 1
---------------+--------+-------------------+------------------------------+------------------------+----------
x..No.. ... | n 0 0 | n 0 0 0 0 0 0 | 2 * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
x.. ... x.. | 4 0 0 | 2 2 0 0 0 0 0 | * n * * * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
xx. ... ...&#x | 2 2 0 | 1 0 2 0 1 0 0 | * * 2n * * * * * * * * * | 0 1 1 0 0 0 1 0 0 0 | 1 0 1 1 0
... ... xo.&#x | 2 1 0 | 0 1 2 0 0 0 0 | * * * n * * * * * * * * | 0 0 2 0 0 0 0 0 2 0 | 1 0 0 2 1
x.o ... ...&#x | 2 0 1 | 1 0 0 2 0 0 0 | * * * * 2n * * * * * * * | 0 0 0 1 1 0 1 0 0 0 | 0 1 1 1 0
... o.x ...&#x | 1 0 2 | 0 0 0 2 0 0 1 | * * * * * 2n * * * * * * | 0 0 0 1 0 1 0 1 0 0 | 0 1 1 0 1
... ... x.o&#x | 2 0 1 | 0 1 0 2 0 0 0 | * * * * * * 2n * * * * * | 0 0 0 0 1 1 0 0 1 0 | 0 1 0 1 1
oooNooo ooo&#x | 1 1 1 | 0 0 1 1 0 1 0 | * * * * * * * 4n * * * * | 0 0 0 0 0 0 1 1 1 0 | 0 0 1 1 1
.x.N.o. ... | 0 n 0 | 0 0 0 0 n 0 0 | * * * * * * * * 1 * * * | 0 2 0 0 0 0 0 0 0 1 | 1 0 2 0 0
.xo ... ...&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * * * n * * | 0 0 0 0 0 0 2 0 0 1 | 0 0 2 1 0
... .ox ...&#x | 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * * * * * n * | 0 0 0 0 0 0 0 2 0 1 | 0 0 2 0 1
..oN..x ... | 0 0 n | 0 0 0 0 0 0 n | * * * * * * * * * * * 1 | 0 0 0 2 0 0 0 0 0 1 | 0 1 2 0 0
---------------+--------+-------------------+------------------------------+------------------------+----------
x..No.. x.. ♦ 2n 0 0 | 2n n 0 0 0 0 0 | 2 n 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
xx.Noo. ...&#x ♦ n n 0 | n 0 n 0 n 0 0 | 1 0 n 0 0 0 0 0 1 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 0
xx. ... xo.&#x ♦ 4 2 0 | 2 2 4 0 1 0 0 | 0 1 2 2 0 0 0 0 0 0 0 0 | * * n * * * * * * * | 1 0 0 1 0
x.oNo.x ...&#x ♦ n 0 n | n 0 0 2n 0 0 n | 1 0 0 0 n n 0 0 0 0 0 1 | * * * 2 * * * * * * | 0 1 1 0 0
x.o ... x.o&#x ♦ 4 0 1 | 2 2 0 4 0 0 0 | 0 1 0 0 2 0 2 0 0 0 0 0 | * * * * n * * * * * | 0 1 0 1 0
... o.x x.o&#x ♦ 2 0 2 | 0 1 0 4 0 0 1 | 0 0 0 0 0 2 2 0 0 0 0 0 | * * * * * n * * * * | 0 1 0 0 1
xxo ... ...&#x ♦ 2 2 1 | 1 0 2 2 1 2 0 | 0 0 1 0 1 0 0 2 0 1 0 0 | * * * * * * 2n * * * | 0 0 1 1 0
... oox ...&#x ♦ 1 1 2 | 0 0 1 2 0 2 1 | 0 0 0 0 0 1 0 2 0 0 1 0 | * * * * * * * 2n * * | 0 0 1 0 1
... ... xoo&#x ♦ 2 1 1 | 0 1 2 2 0 1 0 | 0 0 0 1 0 0 1 2 0 0 0 0 | * * * * * * * * 2n * | 0 0 0 1 1
.xoN.ox ...&#x ♦ 0 n n | 0 0 0 0 n 2n n | 0 0 0 0 0 0 0 0 1 n n 1 | * * * * * * * * * 1 | 0 0 2 0 0
---------------+--------+-------------------+------------------------------+------------------------+----------
xx.Noo. xo.&#x ♦ 2n n 0 | 2n n 2n 0 n 0 0 | 2 n 2n n 0 0 0 0 1 0 0 0 | 1 2 n 0 0 0 0 0 0 0 | 1 * * * *
x.oNo.x x.o&#x ♦ 2n 0 n | 2n n 0 4n 0 0 n | 2 n 0 0 2n 2n 2n 0 0 0 0 1 | 1 0 0 2 n n 0 0 0 0 | * 1 * * *
xxoNoox ...&#x ♦ n n n | n 0 n 2n n 2n n | 1 0 n 0 n n 0 2n 1 n n 1 | 0 1 0 1 0 0 n n 0 1 | * * 2 * *
xxo ... xoo&#x ♦ 4 2 1 | 2 2 4 4 1 2 0 | 0 1 2 2 2 0 2 4 0 1 0 0 | 0 0 1 0 1 0 2 0 2 0 | * * * n *
... oox xoo&#x ♦ 2 1 2 | 0 1 2 4 0 2 1 | 0 0 0 1 0 2 2 4 0 0 1 0 | 0 0 0 0 0 1 0 2 2 0 | * * * * n
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