Acronym n,cube-dip
Name n-gon - cube duoprism
Circumradius sqrt[3/4+1/(4 sin2(π/n))]
Especially tracube (n=3)   pent (n=4)   pecube (n=5)   hacube (n=6)   ocube (n=8)   dacube (n=10)   twacube (n=12)  
Confer
more general:
n,m-dippip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xno o3o4x   (n>2)

. . . . . | 8n |  2   3 | 1   6  3 |  3  6 1 | 3 2
----------+----+--------+----------+---------+----
x . . . . |  2 | 8n   * | 1   3  0 |  3  3 0 | 3 1
. . . . x |  2 |  * 12n | 0   2  2 |  1  4 1 | 2 2
----------+----+--------+----------+---------+----
xno . . . |  n |  n   0 | 8   *  * |  3  0 0 | 3 0
x . . . x |  4 |  2   2 | * 12n  * |  1  2 0 | 2 1
. . . o4x |  4 |  0   4 | *   * 6n |  0  2 1 | 1 2
----------+----+--------+----------+---------+----
xno . . x  2n | 2n   n | 2   n  0 | 12  * * | 2 0
x . . o4x   8 |  4   8 | 0   4  2 |  * 6n * | 1 1
. . o3o4x   8 |  0  12 | 0   0  6 |  *  * n | 0 2
----------+----+--------+----------+---------+----
xno . o4x  4n | 4n  4n | 4  4n  n |  4  n 0 | 6 *
x . o3o4x  16 |  8  24 | 0  12 12 |  0  6 2 | * n

x x4o xno   (n>2)

. . . . . | 8n |  1  2  2 |  2  2  1  4 1 | 1  4 1  2 2 | 2 2 1
----------+----+----------+---------------+-------------+------
x . . . . |  2 | 4n  *  * |  2  2  0  0 0 | 1  4 1  0 0 | 2 2 0
. x . . . |  2 |  * 8n  * |  1  0  1  2 0 | 1  2 0  2 1 | 2 1 1
. . . x . |  2 |  *  * 8n |  0  1  0  2 1 | 0  2 1  1 2 | 1 2 1
----------+----+----------+---------------+-------------+------
x x . . . |  4 |  2  2  0 | 4n  *  *  * * | 1  2 0  0 0 | 2 1 0
x . . x . |  4 |  2  0  2 |  * 4n  *  * * | 0  2 1  0 0 | 1 2 0
. x4o . . |  4 |  0  4  0 |  *  * 2n  * * | 1  0 0  2 0 | 2 0 1
. x . x . |  4 |  0  2  2 |  *  *  * 8n * | 0  1 0  1 1 | 1 1 1
. . . xno |  n |  0  0  n |  *  *  *  * 8 | 0  0 1  0 2 | 0 2 1
----------+----+----------+---------------+-------------+------
x x4o . .   8 |  4  8  0 |  4  0  2  0 0 | n  * *  * * | 2 0 0
x x . x .   8 |  4  4  4 |  2  2  0  2 0 | * 4n *  * * | 1 1 0
x . . xno  2n |  n  0 2n |  0  n  0  0 2 | *  * 4  * * | 0 2 0
. x4o x .   8 |  0  8  4 |  0  0  2  4 0 | *  * * 2n * | 1 0 1
. x . xno  2n |  0  n 2n |  0  0  0  n 2 | *  * *  * 8 | 0 1 1
----------+----+----------+---------------+-------------+------
x x4o x .  16 |  8 16  8 |  8  4  4  8 0 | 2  4 0  2 0 | n * *
x x . xno  4n | 2n 2n 4n |  n 2n  0 2n 4 | 0  n 2  0 2 | * 4 *
. x4o xno  4n |  0 4n 4n |  0  0  n 4n 4 | 0  0 0  n 4 | * * 2

x x x xno   (n>2)

. . . . . | 8n |  1  1  1  2 |  1  1  2  1  2  2 1 | 1  2  2 1  2 1 1 | 2 1 1 1
----------+----+-------------+---------------------+------------------+--------
x . . . . |  2 | 4n  *  *  * |  1  1  2  0  0  0 0 | 1  2  2 1  0 0 0 | 2 1 1 0
. x . . . |  2 |  * 4n  *  * |  1  0  0  1  2  0 0 | 1  2  0 0  2 1 0 | 2 1 0 1
. . x . . |  2 |  *  * 4n  * |  0  1  0  1  0  2 0 | 1  0  2 0  2 0 1 | 2 0 1 1
. . . x . |  2 |  *  *  * 8n |  0  0  1  0  1  1 1 | 0  1  1 1  1 1 1 | 1 1 1 1
----------+----+-------------+---------------------+------------------+--------
x x . . . |  4 |  2  2  0  0 | 2n  *  *  *  *  * * | 1  2  0 0  0 0 0 | 2 1 0 0
x . x . . |  4 |  2  0  2  0 |  * 2n  *  *  *  * * | 1  0  2 0  0 0 0 | 2 0 1 0
x . . x . |  4 |  2  0  0  2 |  *  * 4n  *  *  * * | 0  1  1 1  0 0 0 | 1 1 1 0
. x x . . |  4 |  0  2  2  0 |  *  *  * 2n  *  * * | 1  0  0 0  2 0 0 | 2 0 0 1
. x . x . |  4 |  0  2  0  2 |  *  *  *  * 4n  * * | 0  1  0 0  1 1 0 | 1 1 0 1
. . x x . |  4 |  0  0  2  2 |  *  *  *  *  * 4n * | 0  0  1 0  1 0 1 | 1 0 1 1
. . . xno |  n |  0  0  0  n |  *  *  *  *  *  * 8 | 0  0  0 1  0 1 1 | 0 1 1 1
----------+----+-------------+---------------------+------------------+--------
x x x . .   8 |  4  4  4  0 |  2  2  0  2  0  0 0 | n  *  * *  * * * | 2 0 0 0
x x . x .   8 |  4  4  0  4 |  2  0  2  0  2  0 0 | * 2n  * *  * * * | 1 1 0 0
x . x x .   8 |  4  0  4  4 |  0  2  2  0  0  2 0 | *  * 2n *  * * * | 1 0 1 0
x . . xno  2n |  n  0  0 2n |  0  0  n  0  0  0 2 | *  *  * 4  * * * | 0 1 1 0
. x x x .   8 |  0  4  4  4 |  0  0  0  2  2  2 0 | *  *  * * 2n * * | 1 0 0 1
. x . xno  2n |  0  n  0 2n |  0  0  0  0  n  0 2 | *  *  * *  * 4 * | 0 1 0 1
. . x xno  2n |  0  0  n 2n |  0  0  0  0  0  n 2 | *  *  * *  * * 4 | 0 0 1 1
----------+----+-------------+---------------------+------------------+--------
x x x x .  16 |  8  8  8  8 |  4  4  4  4  4  4 0 | 2  2  2 0  2 0 0 | n * * *
x x . xno  4n | 2n 2n  0 4n |  n  0 2n  0 2n  0 4 | 0  n  0 2  0 2 0 | * 2 * *
x . x xno  4n | 2n  0 2n 4n |  0  n 2n  0  0 2n 4 | 0  0  n 2  0 0 2 | * * 2 *
. x x xno  4n |  0 2n 2n 4n |  0  0  0  n 2n 2n 4 | 0  0  0 0  n 2 2 | * * * 2

xx4oo xxnoo&#x   (n>2)   → height = 1
({4}{n}-dip || {4}{n}-dip)

o.4o. o.no.    | 4n  * |  2  2  1  0  0 | 1  4 1  2  2 0  0 0 | 2 2 1  4 1 0 0 | 1 2 2 0
.o4.o .on.o    |  * 4n |  0  0  1  2  2 | 0  0 0  2  2 1  4 1 | 0 0 1  4 1 2 2 | 0 2 2 1
---------------+-------+----------------+---------------------+----------------+--------
x. .. .. ..    |  2  0 | 4n  *  *  *  * | 1  2 0  1  0 0  0 0 | 2 1 1  2 0 0 0 | 1 2 1 0
.. .. x. ..    |  2  0 |  * 4n  *  *  * | 0  2 1  0  1 0  0 0 | 1 2 0  2 1 0 0 | 1 1 2 0
oo4oo oonoo&#x |  1  1 |  *  * 4n  *  * | 0  0 0  2  2 0  0 0 | 0 0 1  4 1 0 0 | 0 2 2 0
.x .. .. ..    |  0  2 |  *  *  * 4n  * | 0  0 0  1  0 1  2 0 | 0 0 1  2 0 2 1 | 0 2 1 1
.. .. .x ..    |  0  2 |  *  *  *  * 4n | 0  0 0  0  1 0  2 1 | 0 0 0  2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.4o. .. ..    |  4  0 |  4  0  0  0  0 | n  * *  *  * *  * * | 2 0 1  0 0 0 0 | 1 2 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * 4n *  *  * *  * * | 1 1 0  1 0 0 0 | 1 1 1 0
.. .. x.no.    |  n  0 |  0  n  0  0  0 | *  * 4  *  * *  * * | 0 2 0  0 1 0 0 | 1 0 2 0
xx .. .. ..&#x |  2  2 |  1  0  2  1  0 | *  * * 4n  * *  * * | 0 0 1  2 0 0 0 | 0 2 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  * 4n *  * * | 0 0 0  2 1 0 0 | 0 1 2 0
.x4.o .. ..    |  0  4 |  0  0  0  4  0 | *  * *  *  * n  * * | 0 0 1  0 0 2 0 | 0 2 0 1
.x .. .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  * * 4n * | 0 0 0  1 0 1 1 | 0 1 1 1
.. .. .xn.o    |  0  n |  0  0  0  0  n | *  * *  *  * *  * 4 | 0 0 0  0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.4o. x. ..      8  0 |  8  4  0  0  0 | 2  4 0  0  0 0  0 0 | n * *  * * * * | 1 1 0 0
x. .. x.no.     2n  0 |  n 2n  0  0  0 | 0  n 2  0  0 0  0 0 | * 4 *  * * * * | 1 0 1 0
xx4oo .. ..&#x   4  4 |  4  0  4  4  0 | 1  0 0  4  0 1  0 0 | * * n  * * * * | 0 2 0 0
xx .. xx ..&#x   4  4 |  2  2  4  2  2 | 0  1 0  2  2 0  1 0 | * * * 4n * * * | 0 1 1 0
.. .. xxnoo&#x   n  n |  0  n  n  0  n | 0  0 1  0  n 0  0 1 | * * *  * 4 * * | 0 0 2 0
.x4.o .x ..      0  8 |  0  0  0  8  4 | 0  0 0  0  0 2  4 0 | * * *  * * n * | 0 1 0 1
.x .. .xn.o      0 2n |  0  0  0  n 2n | 0  0 0  0  0 0  n 2 | * * *  * * * 4 | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.4o. x.no.     4n  0 | 4n 4n  0  0  0 | n 4n 4  0  0 0  0 0 | n 4 0  0 0 0 0 | 1 * * *
xx4oo xx ..&#x   8  8 |  8  4  8  8  4 | 2  4 0  8  4 2  4 0 | 1 0 2  4 0 1 0 | * n * *
xx .. xxnoo&#x  2n 2n |  n 2n 2n  n 2n | 0  n 2  n 2n 0  n 2 | 0 1 0  n 2 0 1 | * * 4 *
.x4.o .xn.o      0 4n |  0  0  0 4n 4n | 0  0 0  0  0 n 4n 4 | 0 0 0  0 0 n 4 | * * * 1

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