Acronym hixip
Name hexateron prism,
vertex figure of roc
|,>,O device line pyramid pyramid pyramid pyramid prism = |>>>>|
Circumradius sqrt(2/3) = 0.816497
Confer
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

x x3o3o3o3o

. . . . . . | 12 | 1  5 |  5 10 | 10 10 | 10  5 | 5 1
------------+----+------+-------+-------+-------+----
x . . . . . |  2 | 6  *   5  0 | 10  0 | 10  0 | 5 0
. x . . . . |  2 | * 30 |  1  4 |  4  6 |  6  4 | 4 1
------------+----+------+-------+-------+-------+----
x x . . . . |  4 | 2  2 | 15  *   4  0 |  6  0 | 4 0
. x3o . . . |  3 | 0  3 |  * 40 |  1  3 |  3  3 | 3 1
------------+----+------+-------+-------+-------+----
x x3o . . .   6 | 3  6 |  3  2 | 20  * |  3  0 | 3 0
. x3o3o . .   4 | 0  6 |  0  4 |  * 30 |  1  2 | 2 1
------------+----+------+-------+-------+-------+----
x x3o3o . .   8 | 4 12 |  6  8 |  4  2 | 15  * | 2 0
. x3o3o3o .   5 | 0 10 |  0 10 |  0  5 |  * 12 | 1 1
------------+----+------+-------+-------+-------+----
x x3o3o3o .  10 | 5 20 | 10 20 | 10 10 |  5  2 | 6 *
. x3o3o3o3o   6 | 0 15 |  0 20 |  0 15 |  0  6 | * 2

xx3oo3oo3oo3oo&#x   → height = 1
(hix || hix)

o.3o.3o.3o.3o.    | 6 * |  5 1  0 | 10  5  0 | 10 10  0 | 5 10 0 | 1 5 0
.o3.o3.o3.o3.o    | * 6 |  0 1  5 |  0  5 10 |  0 10 10 | 0 10 5 | 0 5 1
------------------+-----+---------+----------+----------+--------+------
x. .. .. .. ..    | 2 0 | 15 *  * |  4  1  0 |  6  4  0 | 4  6 0 | 1 4 0
oo3oo3oo3oo3oo&#x | 1 1 |  * 6  *   0  5  0 |  0 10  0 | 0 10 0 | 0 5 0
.x .. .. .. ..    | 0 2 |  * * 15 |  0  1  4 |  0  4  6 | 0  6 4 | 0 4 1
------------------+-----+---------+----------+----------+--------+------
x.3o. .. .. ..    | 3 0 |  3 0  0 | 20  *  * |  3  1  0 | 3  3 0 | 1 3 0
xx .. .. .. ..&#x | 2 2 |  1 2  1 |  * 15  *   0  4  0 | 0  6 0 | 0 4 0
.x3.o .. .. ..    | 0 3 |  0 0  3 |  *  * 20 |  0  1  3 | 0  3 3 | 0 3 1
------------------+-----+---------+----------+----------+--------+------
x.3o.3o. .. ..     4 0 |  6 0  0 |  4  0  0 | 15  *  * | 2  1 0 | 1 2 0
xx3oo .. .. ..&#x  3 3 |  3 3  3 |  1  3  1 |  * 20  * | 0  3 0 | 0 3 0
.x3.o3.o .. ..     0 4 |  0 0  6 |  0  0  4 |  *  * 15 | 0  1 2 | 0 2 1
------------------+-----+---------+----------+----------+--------+------
x.3o.3o.3o. ..     5 0 | 10 0  0 | 10  0  0 |  5  0  0 | 6  * * | 1 1 0
xx3oo3oo .. ..&#x  4 4 |  6 4  6 |  4  6  4 |  1  4  1 | * 15 * | 0 2 0
.x3.o3.o3.o ..     0 5 |  0 0 10 |  0  0 10 |  0  0  5 | *  * 6 | 0 1 1
------------------+-----+---------+----------+----------+--------+------
x.3o.3o.3o.3o.     6 0 | 15 0  0 | 20  0  0 | 15  0  0 | 6  0 0 | 1 * *
xx3oo3oo3oo ..&#x  5 5 | 10 5 10 | 10 10 10 |  5 10  5 | 1  5 1 | * 6 *
.x3.o3.o3.o3.o     0 6 |  0 0 15 |  0  0 20 |  0  0 15 | 0  0 6 | * * 1

xx ox3oo3oo3oo&#x   → height = sqrt(3/5) = 0.774597
(line || penp)

o. o.3o.3o.3o.    | 2  * | 1  5 0  0 | 5 10  0  0 | 10 10  0  0 | 10  5 0 0 | 5 1 0
.o .o3.o3.o3.o    | * 10 | 0  1 1  4 | 1  4  4  6 |  4  6  6  4 |  6  4 4 1 | 4 1 1
------------------+------+-----------+------------+-------------+-----------+------
x. .. .. .. ..    | 2  0 | 1  * *  *  5  0  0  0 | 10  0  0  0 | 10  0 0 0 | 5 0 0
oo oo3oo3oo3oo&#x | 1  1 | * 10 *  * | 1  4  0  0 |  4  6  0  0 |  6  4 0 0 | 4 1 0
.x .. .. .. ..    | 0  2 | *  * 5  *  1  0  4  0 |  4  0  6  0 |  6  0 4 0 | 4 0 1
.. .x .. .. ..    | 0  2 | *  * * 20 | 0  1  1  3 |  1  3  3  3 |  3  3 3 1 | 3 1 1
------------------+------+-----------+------------+-------------+-----------+------
xx .. .. .. ..&#x | 2  2 | 1  2 1  0 | 5  *  *  *   4  0  0  0 |  6  0 0 0 | 4 0 0
.. ox .. .. ..&#x | 1  2 | 0  2 0  1 | * 20  *  * |  1  3  0  0 |  3  3 0 0 | 3 1 0
.x .x .. .. ..    | 0  4 | 0  0 2  2 | *  * 10  *   1  0  3  0 |  3  0 3 0 | 3 0 1
.. .x3.o .. ..    | 0  3 | 0  0 0  3 | *  *  * 20 |  0  1  1  2 |  1  2 2 1 | 2 1 1
------------------+------+-----------+------------+-------------+-----------+------
xx ox .. .. ..&#x  2  4 | 1  4 2  2 | 2  2  1  0 | 10  *  *  * |  3  0 0 0 | 3 0 0
.. ox3oo .. ..&#x  1  3 | 0  3 0  3 | 0  3  0  1 |  * 20  *  * |  1  2 0 0 | 2 1 0
.x .x3.o .. ..     0  6 | 0  0 3  6 | 0  0  3  2 |  *  * 10  * |  1  0 2 0 | 2 0 1
.. .x3.o3.o ..     0  4 | 0  0 0  6 | 0  0  0  4 |  *  *  * 10 |  0  1 1 1 | 1 1 1
------------------+------+-----------+------------+-------------+-----------+------
xx ox3oo .. ..&#x  2  6 | 1  6 3  6 | 3  6  3  2 |  3  2  1  0 | 10  * * * | 2 0 0
.. ox3oo3oo ..&#x  1  4 | 0  4 0  6 | 0  6  0  4 |  0  4  0  1 |  * 10 * * | 1 1 0
.x .x3.o3.o ..     0  8 | 0  0 4 12 | 0  0  6  8 |  0  0  4  2 |  *  * 5 * | 1 0 1
.. .x3.o3.o3.o     0  5 | 0  0 0 10 | 0  0  0 10 |  0  0  0  5 |  *  * * 2 | 0 1 1
------------------+------+-----------+------------+-------------+-----------+------
xx ox3oo3oo ..&#x  2  8 | 1  8 4 12 | 4 12  6  8 |  6  8  4  2 |  4  2 1 0 | 5 * *
.. ox3oo3oo3oo&#x  1  5 | 0  5 0 10 | 0 10  0 10 |  0 10  0  5 |  0  5 0 1 | * 2 *
.x .x3.o3.o3.o     0 10 | 0  0 5 20 | 0  0 10 20 |  0  0 10 10 |  0  0 5 2 | * * 1

xx xo3oo ox3oo&#x   → height = 1/sqrt(3) = 0.577350
(trip || (not fully) ortho trip)

o. o.3o. o.3o.    | 6 * | 1 2  3 0 0 | 2 1 3  6  3 0 0 | 1 6 3 3  6 1 0 | 3 6 1 3 2 | 3 2 1
.o .o3.o .o3.o    | * 6 | 0 0  3 1 2 | 0 0 3  3  6 2 1 | 0 3 6 1  6 3 1 | 1 6 3 2 3 | 2 3 1
------------------+-----+------------+-----------------+----------------+-----------+------
x. .. .. .. ..    | 2 0 | 3 *  * * *  2 0 3  0  0 0 0 | 1 6 3 0  0 0 0 | 3 6 1 0 0 | 3 2 0
.. x. .. .. ..    | 2 0 | * 6  * * * | 1 1 0  3  0 0 0 | 1 3 0 3  3 0 0 | 3 3 0 3 1 | 3 1 1
oo oo3oo oo3oo&#x | 1 1 | * * 18 * * | 0 0 1  2  2 0 0 | 0 2 2 1  4 1 0 | 1 4 1 2 2 | 2 2 1
.x .. .. .. ..    | 0 2 | * *  * 3 *  0 0 3  0  0 2 0 | 0 3 6 0  0 0 1 | 1 6 3 0 0 | 2 3 0
.. .. .. .x ..    | 0 2 | * *  * * 6 | 0 0 0  0  3 1 1 | 0 0 3 0  3 3 1 | 0 3 3 1 3 | 1 3 1
------------------+-----+------------+-----------------+----------------+-----------+------
x. x. .. .. ..    | 4 0 | 2 2  0 0 0 | 3 * *  *  * * *  1 3 0 0  0 0 0 | 3 3 0 0 0 | 3 1 0
.. x.3o. .. ..    | 3 0 | 0 3  0 0 0 | * 2 *  *  * * * | 1 0 0 3  0 0 0 | 3 0 0 3 0 | 3 0 1
xx .. .. .. ..&#x | 2 2 | 1 0  2 1 0 | * * 9  *  * * *  0 2 2 0  0 0 0 | 1 4 1 0 0 | 2 2 0
.. xo .. .. ..&#x | 2 1 | 0 1  2 0 0 | * * * 18  * * * | 0 1 0 1  2 0 0 | 1 2 0 2 1 | 2 1 1
.. .. .. ox ..&#x | 1 2 | 0 0  2 0 1 | * * *  * 18 * * | 0 0 1 0  2 1 0 | 0 2 1 1 2 | 1 2 1
.x .. .. .x ..    | 0 4 | 0 0  0 2 2 | * * *  *  * 3 *  0 0 3 0  0 0 1 | 0 3 3 0 0 | 1 3 0
.. .. .. .x3.o    | 0 3 | 0 0  0 0 3 | * * *  *  * * 2 | 0 0 0 0  0 3 1 | 0 0 3 0 3 | 0 3 1
------------------+-----+------------+-----------------+----------------+-----------+------
x. x.3o. .. ..     6 0 | 3 6  0 0 0 | 3 2 0  0  0 0 0 | 1 * * *  * * * | 3 0 0 0 0 | 3 0 0
xx xo .. .. ..&#x  4 2 | 2 2  4 1 0 | 1 0 2  2  0 0 0 | * 9 * *  * * * | 1 2 0 0 0 | 2 1 0
xx .. .. ox ..&#x  2 4 | 1 0  4 2 2 | 0 0 2  0  2 1 0 | * * 9 *  * * * | 0 2 1 0 0 | 1 2 0
.. xo3oo .. ..&#x  3 1 | 0 3  3 0 0 | 0 1 0  3  0 0 0 | * * * 6  * * * | 1 0 0 2 0 | 2 0 1
.. xo .. ox ..&#x  2 2 | 0 1  4 0 1 | 0 0 0  2  2 0 0 | * * * * 18 * * | 0 1 0 1 1 | 1 1 1
.. .. .. ox3oo&#x  1 3 | 0 0  3 0 3 | 0 0 0  0  3 0 1 | * * * *  * 6 * | 0 0 1 0 2 | 0 2 1
.x .. .. .x3.o     0 6 | 0 0  0 3 6 | 0 0 0  0  0 3 2 | * * * *  * * 1 | 0 0 3 0 0 | 0 3 0
------------------+-----+------------+-----------------+----------------+-----------+------
xx xo3oo .. ..&#x  6 2 | 3 6  6 1 0 | 3 2 3  6  0 0 0 | 1 3 0 2  0 0 0 | 3 * * * * | 2 0 0
xx xo .. ox ..&#x  4 4 | 2 2  8 2 2 | 1 0 4  4  4 1 0 | 0 2 2 0  2 0 0 | * 9 * * * | 1 1 0
xx .. .. ox3oo&#x  2 6 | 1 0  6 3 6 | 0 0 3  0  6 3 2 | 0 0 3 0  0 2 1 | * * 3 * * | 0 2 0
.. xo3oo ox ..&#x  3 2 | 0 3  6 0 1 | 0 1 0  6  3 0 0 | 0 0 0 2  3 0 0 | * * * 6 * | 1 0 1
.. xo .. ox3oo&#x  2 3 | 0 1  6 0 3 | 0 0 0  3  6 0 1 | 0 0 0 0  3 2 0 | * * * * 6 | 0 1 1
------------------+-----+------------+-----------------+----------------+-----------+------
xx xo3oo ox ..&#x  6 4 | 3 6 12 2 2 | 3 2 6 12  6 1 0 | 1 6 3 4  6 0 0 | 2 3 0 2 0 | 3 * *
xx xo .. ox3oo&#x  4 6 | 2 2 12 3 6 | 1 0 6  6 12 3 2 | 0 3 6 0  6 4 1 | 0 3 2 0 2 | * 3 *
.. xo3oo ox3oo&#x  3 3 | 0 3  9 0 3 | 0 1 0  9  9 0 1 | 0 0 0 3  9 3 0 | 0 0 0 3 3 | * * 2

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