n/d-grammal - n/d-antiprismatic wedge,
{n/d} || gyro n/d-prism
- general polytopal classes:
- segmentochora
| Acronym | n/d-af |
| Name |
n/d-grammal antifastegium, n/d-grammal - n/d-antiprismatic wedge, {n/d} || gyro n/d-prism |
| Segmentochoron display |
|
| Circumradius | sqrt[(1+2 cos(π d/n)-2 cos2(π d/n))/(2+4 cos(π d/n)-6 cos2(π d/n))] |
| Face vector | 3n, 8n, 7n+3, 2n+3 |
| Especially | n-af (d=1) squasc (n=2,d=1) traf (n=3,d=1) squaf (n=4,d=1) paf (n=5,d=1) stafe (n=5,d=2) haf (n=6,d=1) oaf (n=8,d=1) daf (n=10,d=1) |
| Confer |
|
Incidence matrix according to Dynkin symbol
xoo-n/d-oxx&#x → height(1,2) = height(1,3) = sqrt[(1+2 cos(π d/n))/(2+2 cos(π d/n))]
height(2,3) = 1
( {n/d} || (dual {n/d} || dual {n/d}) )
o.. o.. | n * * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o. .o. | * n * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o ..o | * * n | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
---------------+-------+---------------+--------------------+----------
x.. ... | 2 0 0 | n * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.-n/d-oo.&#x | 1 1 0 | * 2n * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o-n/d-o.o&#x | 1 0 1 | * * 2n * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x. | 0 2 0 | * * * n * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo-n/d-.oo&#x | 0 1 1 | * * * * n * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x | 0 0 2 | * * * * * n | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
---------------+-------+---------------+--------------------+----------
x..-n/d-o.. | n 0 0 | n 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * n * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * n * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * n * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * n * * * * | 0 1 0 1 0
ooo-n/d-ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 2n * * * | 0 0 1 1 0
.o.-n/d-.x. | 0 n 0 | 0 0 0 n 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * n * | 0 0 0 1 1
..o-n/d-..x | 0 0 n | 0 0 0 0 0 n | * * * * * * * * 1 | 0 1 0 0 1
---------------+-------+---------------+--------------------+----------
xo.-n/d-ox.&#x ♦ n n 0 | n 2n 0 n 0 0 | 1 n n 0 0 0 1 0 0 | 1 * * * *
x.o-n/d-o.x&#x ♦ n 0 n | n 0 2n 0 0 n | 1 0 0 n n 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * n * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * n *
.oo-n/d-.xx&#x ♦ 0 n n | 0 0 0 n n n | 0 0 0 0 0 0 1 n 1 | * * * * 1
xo-n/d-ox ox&#x → height = sqrt[(1+3 cos(π d/n))/(4+4 cos(π d/n))]
({n/d} || gyro n/d-p)
o. o. o. | n * | 2 4 0 0 | 1 4 2 2 0 0 | 2 2 1 0
.o .o .o | * 2n | 0 2 2 1 | 0 1 2 2 1 2 | 1 1 2 1
----------------+------+-----------+----------------+--------
x. .. .. | 2 0 | n * * * | 1 2 0 0 0 0 | 2 1 0 0
oo-n/d-oo oo&#x | 1 1 | * 4n * * | 0 1 1 1 0 0 | 1 1 1 0
.. .x .. | 0 2 | * * 2n * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x | 0 2 | * * * n | 0 0 0 2 0 2 | 0 1 2 1
----------------+------+-----------+----------------+--------
x.-n/d-o. .. | n 0 | n 0 0 0 | 1 * * * * * | 2 0 0 0
xo .. ..&#x | 2 1 | 1 2 0 0 | * 2n * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0 2 1 0 | * * 2n * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0 2 0 1 | * * * 2n * * | 0 1 1 0
.o-n/d-.x .. | 0 n | 0 0 n 0 | * * * * 2 * | 1 0 0 1
.. .x .x | 0 4 | 0 0 2 2 | * * * * * n | 0 0 1 1
----------------+------+-----------+----------------+--------
xo-n/d-ox ..&#x ♦ n n | n 2n n 0 | 1 n n 0 1 0 | 2 * * *
xo .. ox&#x ♦ 2 2 | 1 4 0 1 | 0 2 0 2 0 0 | * n * *
.. ox ox&#x ♦ 1 4 | 0 4 2 2 | 0 0 2 2 0 1 | * * n *
.o-n/d-.x .x ♦ 0 2n | 0 0 2n n | 0 0 0 0 2 n | * * * 1
{n/d} || n/d-ap → height = sqrt[(1+3 cos(π d/n))/(2+4 cos(π d/n))]
o.. o.. | n * * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o. .o. | * n * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o ..o | * * n | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
---------------+-------+---------------+--------------------+----------
x.. ... | 2 0 0 | n * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.-n/d-oo.&#x | 1 1 0 | * 2n * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o-n/d-o.o&#x | 1 0 1 | * * 2n * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x. | 0 2 0 | * * * n * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo-n/d-.oo&#x | 0 1 1 | * * * * n * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x | 0 0 2 | * * * * * n | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
---------------+-------+---------------+--------------------+----------
x..-n/d-o.. | n 0 0 | n 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * n * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * n * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * n * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * n * * * * | 0 1 0 1 0
ooo-n/d-ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 2n * * * | 0 0 1 1 0
.o.-n/d-.x. | 0 n 0 | 0 0 0 n 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * n * | 0 0 0 1 1
..o-n/d-..x | 0 0 n | 0 0 0 0 0 n | * * * * * * * * 1 | 0 1 0 0 1
---------------+-------+---------------+--------------------+----------
xo.-n/d-ox.&#x ♦ n n 0 | n 2n 0 n 0 0 | 1 n n 0 0 0 1 0 0 | 1 * * * *
x.o-n/d-o.x&#x ♦ n 0 n | n 0 2n 0 0 n | 1 0 0 n n 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * n * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * n *
.oo-n/d-.xx&#x ♦ 0 n n | 0 0 0 n n n | 0 0 0 0 0 0 1 n 1 | * * * * 1
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