n-gon - 2n-prismatic wedge,
n-gonal magnabicupolaic ring,
{n} || 2n-prism,
{2n} || n-cupola
in approx. ASCII-art
x-n-o
x-n-x x-n-x
(at margins)
- general polytopal classes:
- segmentochora
| Acronym | n-puf |
| Name |
n-gonal pucofastegium, n-gon - 2n-prismatic wedge, n-gonal magnabicupolaic ring, {n} || 2n-prism, {2n} || n-cupola |
| Segmentochoron display |
|
| Circumradius | sqrt[(2 cos2(π/n)-2 cos(π/n)-3)/(6 cos2(π/n)-2)] |
|
Lace city in approx. ASCII-art |
x-n-o
x-n-x x-n-x
|
|
Dihedral angles
(at margins) | |
| Face vector | 5n, 11n, 8n+3, 2n+3 |
| Especially | squippyp (n=2)* {3} || hip (n=3) {4} || op (n=4) {5} || dip (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.
"Puco" in the naming, based to the acronym, was chosen by Bowers as inverted usage, i.e. as spoonerism to "cupo" in cupolae, cf. n-cuf.
Incidence matrix according to Dynkin symbol
xxx-n-oxx&#x → height(1,2) = height(1,3) = sqrt[4 - 1/sin2(π/n)]/2
height(2,3) = 1
o..-n-o.. | n * * | 2 2 2 0 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 | 1 1 2 1 0
.o.-n-.o. | * 2n * | 0 1 0 1 1 1 0 0 | 0 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1
..o-n-..o | * * 2n | 0 0 1 0 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
-------------+---------+--------------------+----------------------+----------
x.. ... | 2 0 0 | n * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
oo.-n-oo.&#x | 1 1 0 | * 2n * * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
o.o-n-o.o&#x | 1 0 1 | * * 2n * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.x. ... | 0 2 0 | * * * n * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x. | 0 2 0 | * * * * n * * * | 0 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1
.oo-n-.oo&#x | 0 1 1 | * * * * * 2n * * | 0 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 0 1 0 1 | 0 1 1 0 1
... ..x | 0 0 2 | * * * * * * * n | 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1
-------------+---------+--------------------+----------------------+----------
x..-n-o.. | n 0 0 | n 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 0 | * n * * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 0 | * * n * * * * * * * | 1 0 0 1 0
x.x ...&#x | 2 0 2 | 1 0 2 0 0 0 1 0 | * * * n * * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 0 0 1 | * * * * n * * * * * | 0 1 0 1 0
ooo-n-ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 0 | * * * * * 2n * * * * | 0 0 1 1 0
.x.-n-.x. | 0 2n 0 | 0 0 0 n n 0 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 0 | * * * * * * * n * * | 0 0 1 0 1
... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 1 | * * * * * * * * n * | 0 0 0 1 1
..x-n-..x | 0 0 2n | 0 0 0 0 0 0 n n | * * * * * * * * * 1 | 0 1 0 0 1
-------------+---------+--------------------+----------------------+----------
xx.-n-ox.&#x ♦ n 2n 0 | n 2n 0 n n 0 0 0 | 1 n n 0 0 0 1 0 0 0 | 1 * * * *
x.x-n-o.x&#x ♦ n 0 2n | n 0 2n 0 0 0 n n | 1 0 0 n n 0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2 2 2 | 1 2 2 1 0 2 1 0 | 0 1 0 1 0 2 0 1 0 0 | * * n * *
... oxx&#x ♦ 1 2 2 | 0 2 2 0 1 2 0 1 | 0 0 1 0 1 2 0 0 1 0 | * * * n *
.xx-n-.xx&#x ♦ 0 2n 2n | 0 0 0 n n 2n n n | 0 0 0 0 0 0 1 n n 1 | * * * * 1
xx-n-ox ox&#x (2 ≤ n < 5.104299) → height = sqrt[3 - 1/sin2(π/n)]/2
({n} || 2n-p)
o.-n-o. o. | n * | 2 4 0 0 0 | 1 4 2 2 0 0 0 | 2 2 1 0
.o-n-.o .o | * 4n | 0 1 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
--------------+------+---------------+------------------+--------
x. .. .. | 2 0 | n * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
oo-n-oo oo&#x | 1 1 | * 4n * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.x .. .. | 0 2 | * * 2n * * | 0 1 0 0 1 1 0 | 1 1 0 1
.. .x .. | 0 2 | * * * 2n * | 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x | 0 2 | * * * * 2n | 0 0 0 1 0 1 1 | 0 1 1 1
--------------+------+---------------+------------------+--------
x.-n-o. .. | n 0 | n 0 0 0 0 | 1 * * * * * * | 2 0 0 0
xx .. ..&#x | 2 2 | 1 2 1 0 0 | * 2n * * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 0 | * * 2n * * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0 2 0 0 1 | * * * 2n * * * | 0 1 1 0
.x-n-.x .. | 0 2n | 0 0 n n 0 | * * * * 2 * * | 1 0 0 1
.x .. .x | 0 4 | 0 0 2 0 2 | * * * * * n * | 0 1 0 1
.. .x .x | 0 4 | 0 0 0 2 2 | * * * * * * n | 0 0 1 1
--------------+------+---------------+------------------+--------
xx-n-ox ..&#x ♦ n 2n | n 2n n n 0 | 1 n n 0 1 0 0 | 2 * * *
xx .. ox&#x ♦ 2 4 | 1 4 2 0 2 | 0 2 0 2 0 1 0 | * n * *
.. ox ox&#x ♦ 1 4 | 0 4 0 2 2 | 0 0 2 2 0 0 1 | * * n *
.x-n-.x .x ♦ 0 4n | 0 0 2n 2n 2n | 0 0 0 0 2 n n | * * * 1
{2n} || n-cu → height = sqrt[3 - 3/(4 sqrt2(π/n))]/2
2n * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
* n * | 0 0 2 0 2 2 0 0 | 0 2 1 0 0 2 1 2 1 0 | 1 0 2 1 1
* * 2n | 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
----------+--------------------+----------------------+----------
2 0 0 | n * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
2 0 0 | * n * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0
1 1 0 | * * 2n * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
1 0 1 | * * * 2n * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
0 2 0 | * * * * n * * * | 0 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1
0 1 1 | * * * * * 2n * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
0 0 2 | * * * * * * n * | 0 0 0 1 0 0 0 1 0 1 | 0 1 1 0 1
0 0 2 | * * * * * * * n | 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1
----------+--------------------+----------------------+----------
2n 0 0 | n n 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
2 2 0 | 1 0 2 0 1 0 0 0 | * n * * * * * * * * | 1 0 1 0 0
2 1 0 | 0 1 2 0 0 0 0 0 | * * n * * * * * * * | 1 0 0 1 0
2 0 2 | 1 0 0 2 0 0 1 0 | * * * n * * * * * * | 0 1 1 0 0
2 0 2 | 0 1 0 2 0 0 0 1 | * * * * n * * * * * | 0 1 0 1 0
1 1 1 | 0 0 1 1 0 1 0 0 | * * * * * 2n * * * * | 0 0 1 1 0
0 n 0 | 0 0 0 0 n 0 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
0 2 2 | 0 0 0 0 1 2 1 0 | * * * * * * * n * * | 0 0 1 0 1
0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * * n * | 0 0 0 1 1
0 0 2n | 0 0 0 0 0 0 n n | * * * * * * * * * 1 | 0 1 0 0 1
----------+--------------------+----------------------+----------
♦ 2n n 0 | n n 2n 0 n 0 0 0 | 1 n n 0 0 0 1 0 0 0 | 1 * * * *
♦ 2n 0 2n | n n 0 2n 0 0 n n | 1 0 0 n n 0 0 0 0 1 | * 1 * * *
♦ 2 2 2 | 1 0 2 2 1 2 1 0 | 0 1 0 1 0 2 0 1 0 0 | * * n * *
♦ 2 1 2 | 0 1 2 2 0 2 0 1 | 0 0 1 0 1 2 0 0 1 0 | * * * n *
♦ 0 n 2n | 0 0 0 0 n 2n n n | 0 0 0 0 0 0 1 n n 1 | * * * * 1
© 2004-2024 | top of page |