Acronym n,pen-dip
Name n-gon - pentachoron duoprism
Circumradius sqrt[1/(4 sin2(π d/n))+2/5]
Confer
general polytopal classes:
segmentopeta  
Especially trapen (n=3)   squapen (n=4)   open (n=8)   stopen (n=8/3)  

Incidence matrix according to Dynkin symbol

xno x3o3o3o   (n>2)

. . . . . . | 5n |  2   4 | 1   8   6 |  4  12  4 |  6  8 1 | 4 2
------------+----+--------+-----------+-----------+---------+----
x . . . . . |  2 | 5n   * | 1   4   0 |  4   6  0 |  6  4 0 | 4 1
. . x . . . |  2 |  * 10n | 0   2   3 |  1   6  3 |  3  6 1 | 3 2
------------+----+--------+-----------+-----------+---------+----
xno . . . . |  n |  n   0 | 5   *   *   4   0  0 |  6  0 0 | 4 0
x . x . . . |  4 |  2   2 | * 10n   * |  1   3  0 |  3  3 0 | 3 1
. . x3o . . |  3 |  0   3 | *   * 10n |  0   2  2 |  1  4 1 | 2 2
------------+----+--------+-----------+-----------+---------+----
xno x . . .  2n | 2n   n | 2   n   0 | 10   *  * |  3  0 0 | 3 0
x . x3o . .   6 |  3   6 | 0   3   2 |  * 10n  * |  1  2 0 | 2 1
. . x3o3o .   4 |  0   6 | 0   0   4 |  *   * 5n |  0  2 1 | 1 2
------------+----+--------+-----------+-----------+---------+----
xno x3o . .  3n | 3n  3n | 3  3n   n |  3   n  0 | 10  * * | 2 0
x . x3o3o .   8 |  4  12 | 0   6   8 |  0   4  2 |  * 5n * | 1 1
. . x3o3o3o   5 |  0  10 | 0   0  10 |  0   0  5 |  *  * n | 0 2
------------+----+--------+-----------+-----------+---------+----
xno x3o3o .  4n | 4n  6n | 4  6n  4n |  6  4n  n |  4  n 0 | 5 *
x . x3o3o3o  10 |  5  20 | 0  10  20 |  0  10 10 |  0  5 2 | * n

xx-n-oo ox3oo3oo&#x   (n>2)   → height = sqrt(5/8) = 0.790569
({n} || (n,tet)-dip)

o.-n-o. o.3o.3o.    | n  * | 2  4  0  0 | 1  8  6 0  0  0 | 4 12  4 0  0 0 | 6  8 1 0 0 | 4 2 0
.o-n-.o .o3.o3.o    | * 4n | 0  1  2  3 | 0  2  3 1  6  3 | 1  6  3 3  6 1 | 3  6 1 3 2 | 3 2 1
--------------------+------+------------+-----------------+----------------+------------+------
x.   .. .. .. ..    | 2  0 | n  *  *  * | 1  4  0 0  0  0 | 4  6  0 0  0 0 | 6  4 0 0 0 | 4 1 0
oo-n-oo oo3oo3oo&#x | 1  1 | * 4n  *  * | 0  2  3 0  0  0 | 1  6  3 0  0 0 | 3  6 1 0 0 | 3 2 0
.x   .. .. .. ..    | 0  2 | *  * 4n  * | 0  1  0 1  3  0 | 1  3  0 3  3 0 | 3  3 0 3 1 | 3 1 1
..   .. .x .. ..    | 0  2 | *  *  * 6n | 0  0  1 0  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
--------------------+------+------------+-----------------+----------------+------------+------
x.-n-o. .. .. ..    | n  0 | n  0  0  0 | 1  *  * *  *  *  4  0  0 0  0 0 | 6  0 0 0 0 | 4 0 0
xx   .. .. .. ..&#x | 2  2 | 1  2  1  0 | * 4n  * *  *  * | 1  3  0 0  0 0 | 3  3 0 0 0 | 3 1 0
..   .. ox .. ..&#x | 1  2 | 0  2  0  1 | *  * 6n *  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x-n-.o .. .. ..    | 0  n | 0  0  n  0 | *  *  * 4  *  *  1  0  0 3  0 0 | 3  0 0 3 0 | 3 0 1
.x   .. .x .. ..    | 0  4 | 0  0  2  2 | *  *  * * 6n  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
..   .. .x3.o ..    | 0  3 | 0  0  0  3 | *  *  * *  * 4n | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
--------------------+------+------------+-----------------+----------------+------------+------
xx-n-oo .. .. ..&#x  n  n | n  n  n  0 | 1  n  0 1  0  0 | 4  *  * *  * * | 3  0 0 0 0 | 3 0 0
xx   .. ox .. ..&#x  2  4 | 1  4  2  2 | 0  2  2 0  1  0 | * 6n  * *  * * | 1  2 0 0 0 | 1 2 0
..   .. ox3oo ..&#x  1  3 | 0  3  0  3 | 0  0  3 0  0  1 | *  * 4n *  * * | 0  2 1 0 0 | 1 2 0
.x-n-.o .x .. ..     0 2n | 0  0 2n  n | 0  0  0 2  n  0 | *  *  * 6  * * | 1  0 0 2 0 | 2 0 1
.x   .. .x3.o ..     0  6 | 0  0  3  6 | 0  0  0 0  3  2 | *  *  * * 4n * | 0  1 0 1 1 | 1 1 1
..   .. .x3.o3.o     0  4 | 0  0  0  6 | 0  0  0 0  0  4 | *  *  * *  * n | 0  0 1 0 2 | 0 2 1
--------------------+------+------------+-----------------+----------------+------------+------
xx-n-oo ox .. ..&#x   n 2n | n 2n 2n  n | 1 2n  n 2  n  0 | 2  n  0 1  0 0 | 6  * * * * | 2 0 0
xx   .. ox3oo ..&#x  2  6 | 1  6  3  6 | 0  3  6 0  3  2 | 0  3  2 0  1 0 | * 4n * * * | 1 1 0
..   .. ox3oo3oo&#x  1  4 | 0  4  0  6 | 0  0  6 0  0  4 | 0  0  4 0  0 1 | *  * n * * | 0 2 0
.x-n-.o .x3.o ..      0 3n | 0  0 3n 3n | 0  0  0 3 3n  n | 0  0  0 3  n 0 | *  * * 4 * | 1 0 1
.x   .. .x3.o3.o     0  8 | 0  0  4 12 | 0  0  0 0  6  8 | 0  0  0 0  4 2 | *  * * * n | 0 1 1
--------------------+------+------------+-----------------+----------------+------------+------
xx-n-oo ox3oo ..&#x  n 3n | n 3n 3n 3n | 1 3n 3n 3 3n  n | 3 3n  n 3  n 0 | 3  n 0 1 0 | 4 * *
xx   .. ox3oo3oo&#x  2  8 | 1  8  4 12 | 0  4 12 0  6  8 | 0  6  8 0  4 2 | 0  4 2 0 1 | * n *
.x-n-.o .x3.o3.o     0 4n | 0  0 4n 6n | 0  0  0 4 6n 4n | 0  0  0 6 4n n | 0  0 0 4 n | * * 1

© 2004-2021
top of page