Acronym haco (old: hicco)
Name hexagon cuboctahedron duoprism
Circumradius sqrt(2) = 1.414214
Confer
more general:
n,co-dip  
segmentotera:
hatricu  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x6o o3x4o

. . . . . | 72 |  2   4 |  1   8  2  2 |  4  4  4 1 | 2 2 2
----------+----+--------+--------------+------------+------
x . . . . |  2 | 72   * |  1   4  0  0 |  4  2  2 0 | 2 2 1
. . . x . |  2 |  * 144 |  0   2  1  1 |  1  2  2 1 | 1 1 2
----------+----+--------+--------------+------------+------
x6o . . . |  6 |  6   0 | 12   *  *  * |  4  0  0 0 | 2 2 0
x . . x . |  4 |  2   2 |  * 144  *  * |  1  1  1 0 | 1 1 1
. . o3x . |  3 |  0   3 |  *   * 48  * |  0  2  0 1 | 1 0 2
. . . x4o |  4 |  0   4 |  *   *  * 36 |  0  0  2 1 | 0 1 2
----------+----+--------+--------------+------------+------
x6o . x .  12 | 12   6 |  2   6  0  0 | 24  *  * * | 1 1 0
x . o3x .   6 |  3   6 |  0   3  2  0 |  * 48  * * | 1 0 1
x . . x4o   8 |  4   8 |  0   4  0  2 |  *  * 36 * | 0 1 1
. . o3x4o  12 |  0  24 |  0   0  8  6 |  *  *  * 6 | 0 0 2
----------+----+--------+--------------+------------+------
x6o o3x .  18 | 18  18 |  3  18  6  0 |  3  6  0 0 | 8 * *
x6o . x4o  24 | 24  24 |  4  24  0  6 |  4  0  6 0 | * 6 *
x . o3x4o  24 | 12  48 |  0  24 16 12 |  0  8  6 2 | * * 6

x3x o3x4o

. . . . . | 72 |  1  1   4 |  1  4  4  2  2 |  4  2  2  2  2 1 | 2 2 1 1
----------+----+-----------+----------------+------------------+--------
x . . . . |  2 | 36  *   * |  1  4  0  0  0 |  4  2  2  0  0 0 | 2 2 1 0
. x . . . |  2 |  * 36   * |  1  0  4  0  0 |  4  0  0  2  2 0 | 2 2 0 1
. . . x . |  2 |  *  * 144 |  0  1  1  1  1 |  1  1  1  1  1 1 | 1 1 1 1
----------+----+-----------+----------------+------------------+--------
x3x . . . |  6 |  3  3   0 | 12  *  *  *  * |  4  0  0  0  0 0 | 2 2 0 0
x . . x . |  4 |  2  0   2 |  * 72  *  *  * |  1  1  1  0  0 0 | 1 1 1 0
. x . x . |  4 |  0  2   2 |  *  * 72  *  * |  1  0  0  1  1 0 | 1 1 0 1
. . o3x . |  3 |  0  0   3 |  *  *  * 48  * |  0  1  0  1  0 1 | 1 0 1 1
. . . x4o |  4 |  0  0   4 |  *  *  *  * 36 |  0  0  1  0  1 1 | 0 1 1 1
----------+----+-----------+----------------+------------------+--------
x3x . x .  12 |  6  6   6 |  2  3  3  0  0 | 24  *  *  *  * * | 1 1 0 0
x . o3x .   6 |  3  0   6 |  0  3  0  2  0 |  * 24  *  *  * * | 1 0 1 0
x . . x4o   8 |  4  0   8 |  0  4  0  0  2 |  *  * 18  *  * * | 0 1 1 0
. x o3x .   6 |  0  3   6 |  0  0  3  2  0 |  *  *  * 24  * * | 1 0 0 1
. x . x4o   8 |  0  4   8 |  0  0  4  0  2 |  *  *  *  * 18 * | 0 1 0 1
. . o3x4o  12 |  0  0  24 |  0  0  0  8  6 |  *  *  *  *  * 6 | 0 0 1 1
----------+----+-----------+----------------+------------------+--------
x3x o3x .  18 |  9  9  18 |  3  9  9  6  0 |  3  3  0  3  0 0 | 8 * * *
x3x . x4o  24 | 12 12  24 |  4 12 12  0  6 |  4  0  3  0  3 0 | * 6 * *
x . o3x4o  24 | 12  0  48 |  0 24  0 16 12 |  0  8  6  0  0 2 | * * 3 *
. x o3x4o  24 |  0 12  48 |  0  0 24 16 12 |  0  0  0  8  6 2 | * * * 3

x6o x3o3x

. . . . . | 72 |  2  2  2 |  1  4  4  1  2  1 |  2  2  2  4  2 1 | 1 2 1 2
----------+----+----------+-------------------+------------------+--------
x . . . . |  2 | 72  *  * |  1  2  2  0  0  0 |  2  2  1  2  1 0 | 1 2 1 1
. . x . . |  2 |  * 72  * |  0  2  0  1  1  0 |  1  0  2  2  0 1 | 1 1 0 2
. . . . x |  2 |  *  * 72 |  0  0  2  0  1  1 |  0  1  0  2  2 1 | 0 1 1 2
----------+----+----------+-------------------+------------------+--------
x6o . . . |  6 |  6  0  0 | 12  *  *  *  *  * |  2  2  0  0  0 0 | 1 2 1 0
x . x . . |  4 |  2  2  0 |  * 72  *  *  *  * |  1  0  1  1  0 0 | 1 1 0 1
x . . . x |  4 |  2  0  2 |  *  * 72  *  *  * |  0  1  0  1  1 0 | 0 1 1 1
. . x3o . |  3 |  0  3  0 |  *  *  * 24  *  * |  0  0  2  0  0 1 | 1 0 0 2
. . x . x |  4 |  0  2  2 |  *  *  *  * 36  * |  0  0  0  2  0 1 | 0 1 0 2
. . . o3x |  3 |  0  0  3 |  *  *  *  *  * 24 |  0  0  0  0  2 1 | 0 0 1 2
----------+----+----------+-------------------+------------------+--------
x6o x . .  12 | 12  6  0 |  2  6  0  0  0  0 | 12  *  *  *  * * | 1 1 0 0
x6o . . x  12 | 12  0  6 |  2  0  6  0  0  0 |  * 12  *  *  * * | 0 1 1 0
x . x3o .   6 |  3  6  0 |  0  3  0  2  0  0 |  *  * 24  *  * * | 1 0 0 1
x . x . x   8 |  4  4  4 |  0  2  2  0  2  0 |  *  *  * 36  * * | 0 1 0 1
x . . o3x   6 |  3  0  6 |  0  0  3  0  0  2 |  *  *  *  * 24 * | 0 0 1 1
. . x3o3x  12 |  0 12 12 |  0  0  0  4  6  4 |  *  *  *  *  * 6 | 0 0 0 2
----------+----+----------+-------------------+------------------+--------
x6o x3o .  18 | 18 18  0 |  3 18  0  6  0  0 |  3  0  6  0  0 0 | 4 * * *
x6o x . x  24 | 24 12 12 |  4 12 12  0  6  0 |  2  2  0  6  0 0 | * 6 * *
x6o . o3x  18 | 18  0 18 |  3  0 18  0  0  6 |  0  3  0  0  6 0 | * * 4 *
x . x3o3x  24 | 12 24 24 |  0 12 12  8 12  8 |  0  0  4  6  4 2 | * * * 6

x3x x3o3x

. . . . . | 72 |  1  1  2  2 |  1  2  2  2  2  1  2  1 |  2  2  1  2  1  1  2  1 1 | 1 2 1 1 1
----------+----+-------------+-------------------------+---------------------------+----------
x . . . . |  2 | 36  *  *  * |  1  2  2  0  0  0  0  0 |  2  2  1  2  1  0  0  0 0 | 1 2 1 1 0
. x . . . |  2 |  * 36  *  * |  1  0  0  2  2  0  0  0 |  2  2  0  0  0  1  2  1 0 | 1 2 1 0 1
. . x . . |  2 |  *  * 72  * |  0  1  0  1  0  1  1  0 |  1  0  1  1  0  1  1  0 1 | 1 1 0 1 1
. . . . x |  2 |  *  *  * 72 |  0  0  1  0  1  0  1  1 |  0  1  0  1  1  0  1  1 1 | 0 1 1 1 1
----------+----+-------------+-------------------------+---------------------------+----------
x3x . . . |  6 |  3  3  0  0 | 12  *  *  *  *  *  *  * |  2  2  0  0  0  0  0  0 0 | 1 2 1 0 0
x . x . . |  4 |  2  0  2  0 |  * 36  *  *  *  *  *  * |  1  0  1  1  0  0  0  0 0 | 1 1 0 1 0
x . . . x |  4 |  2  0  0  2 |  *  * 36  *  *  *  *  * |  0  1  0  1  1  0  0  0 0 | 0 1 1 1 0
. x x . . |  4 |  0  2  2  0 |  *  *  * 36  *  *  *  * |  1  0  0  0  0  1  1  0 0 | 1 1 0 0 1
. x . . x |  4 |  0  2  0  2 |  *  *  *  * 36  *  *  * |  0  1  0  0  0  0  1  1 0 | 0 1 1 0 1
. . x3o . |  3 |  0  0  3  0 |  *  *  *  *  * 24  *  * |  0  0  1  0  0  1  0  0 1 | 1 0 0 1 1
. . x . x |  4 |  0  0  2  2 |  *  *  *  *  *  * 36  * |  0  0  0  1  0  0  1  0 1 | 0 1 0 1 1
. . . o3x |  3 |  0  0  0  3 |  *  *  *  *  *  *  * 24 |  0  0  0  0  1  0  0  1 1 | 0 0 1 1 1
----------+----+-------------+-------------------------+---------------------------+----------
x3x x . .  12 |  6  6  6  0 |  2  3  0  3  0  0  0  0 | 12  *  *  *  *  *  *  * * | 1 1 0 0 0
x3x . . x  12 |  6  6  0  6 |  2  0  3  0  3  0  0  0 |  * 12  *  *  *  *  *  * * | 0 1 1 0 0
x . x3o .   6 |  3  0  6  0 |  0  3  0  0  0  2  0  0 |  *  * 12  *  *  *  *  * * | 1 0 0 1 0
x . x . x   8 |  4  0  4  4 |  0  2  2  0  0  0  2  0 |  *  *  * 18  *  *  *  * * | 0 1 0 1 0
x . . o3x   6 |  3  0  0  6 |  0  0  3  0  0  0  0  2 |  *  *  *  * 12  *  *  * * | 0 0 1 1 0
. x x3o .   6 |  0  3  6  0 |  0  0  0  3  0  2  0  0 |  *  *  *  *  * 12  *  * * | 1 0 0 0 1
. x x . x   8 |  0  4  4  4 |  0  0  0  2  2  0  2  0 |  *  *  *  *  *  * 18  * * | 0 1 0 0 1
. x . o3x   6 |  0  3  0  6 |  0  0  0  0  3  0  0  2 |  *  *  *  *  *  *  * 12 * | 0 0 1 0 1
. . x3o3x  12 |  0  0 12 12 |  0  0  0  0  0  4  6  4 |  *  *  *  *  *  *  *  * 6 | 0 0 0 1 1
----------+----+-------------+-------------------------+---------------------------+----------
x3x x3o .  18 |  9  9 18  0 |  3  9  0  9  0  6  0  0 |  3  0  3  0  0  3  0  0 0 | 4 * * * *
x3x x . x  24 | 12 12 12 12 |  4  6  6  6  6  0  6  0 |  2  2  0  3  0  0  3  0 0 | * 6 * * *
x3x . o3x  18 |  9  9  0 18 |  3  0  9  0  9  0  0  6 |  0  3  0  0  3  0  0  3 0 | * * 4 * *
x . x3o3x  24 | 12  0 24 24 |  0 12 12  0  0  8 12  8 |  0  0  4  6  4  0  0  0 2 | * * * 3 *
. x x3o3x  24 |  0 12 24 24 |  0  0  0 12 12  8 12  8 |  0  0  0  0  0  4  6  4 2 | * * * * 3

oxx3xxo xxx3xxx&#amp;#xt   → both heights = sqrt(2/3) = 0.816497
(thiddip || pseudo hiddip || gyro thiddip)

o..3o.. o..3o..     & | 36  * |  2  1  1  2  0  0  0 |  1  2  2 1  1  2  2  2  0  0 0 | 1 1 2 1  1  1  2  2  2 0 | 1 1 1 1 2
.o.3.o. .o.3.o.       |  * 36 |  0  0  0  2  2  1  1 |  0  0  0 0  2  2  2  2  2  2 1 | 0 0 0 1  2  2  2  2  2 2 | 0 1 1 2 2
----------------------+-------+----------------------+--------------------------------+--------------------------+----------
... x.. ... ...     & |  2  0 | 36  *  *  *  *  *  * |  1  1  1 0  0  1  0  0  0  0 0 | 1 1 1 1  0  0  1  1  0 0 | 1 1 1 0 1
... ... x.. ...     & |  2  0 |  * 18  *  *  *  *  * |  0  2  0 1  0  0  2  0  0  0 0 | 1 0 2 0  1  0  2  0  2 0 | 1 1 0 1 2
... ... ... x..     & |  2  0 |  *  * 18  *  *  *  * |  0  0  2 1  0  0  0  2  0  0 0 | 0 1 2 0  0  1  0  2  2 0 | 1 0 1 1 2
oo.3oo. oo.3oo.&#x  & |  1  1 |  *  *  * 72  *  *  * |  0  0  0 0  1  1  1  1  0  0 0 | 0 0 0 1  1  1  1  1  1 0 | 0 1 1 1 1
.x. ... ... ...     & |  0  2 |  *  *  *  * 36  *  * |  0  0  0 0  1  1  0  0  1  1 0 | 0 0 0 1  1  1  1  1  0 1 | 0 1 1 1 1
... ... .x. ...     & |  0  2 |  *  *  *  *  * 18  * |  0  0  0 0  0  0  2  0  2  0 1 | 0 0 0 0  2  0  2  0  2 2 | 0 1 0 2 2
... ... ... .x.     & |  0  2 |  *  *  *  *  *  * 18 |  0  0  0 0  0  0  0  2  0  2 1 | 0 0 0 0  0  2  0  2  2 2 | 0 0 1 2 2
----------------------+-------+----------------------+--------------------------------+--------------------------+----------
o..3x.. ... ...     & |  3  0 |  3  0  0  0  0  0  0 | 12  *  * *  *  *  *  *  *  * * | 1 1 0 1  0  0  0  0  0 0 | 1 1 1 0 0
... x.. x.. ...     & |  4  0 |  2  2  0  0  0  0  0 |  * 18  * *  *  *  *  *  *  * * | 1 0 1 0  0  0  1  0  0 0 | 1 1 0 0 1
... x.. ... x..     & |  4  0 |  2  0  2  0  0  0  0 |  *  * 18 *  *  *  *  *  *  * * | 0 1 1 0  0  0  0  1  0 0 | 1 0 1 0 1
... ... x..3x..     & |  6  0 |  0  3  3  0  0  0  0 |  *  *  * 6  *  *  *  *  *  * * | 0 0 2 0  0  0  0  0  2 0 | 1 0 0 1 2
ox. ... ... ...&#x  & |  1  2 |  0  0  0  2  1  0  0 |  *  *  * * 36  *  *  *  *  * * | 0 0 0 1  1  1  0  0  0 0 | 0 1 1 1 0
... xx. ... ...&#x  & |  2  2 |  1  0  0  2  1  0  0 |  *  *  * *  * 36  *  *  *  * * | 0 0 0 1  0  0  1  1  0 0 | 0 1 1 0 1
... ... xx. ...&#x  & |  2  2 |  0  1  0  2  0  1  0 |  *  *  * *  *  * 36  *  *  * * | 0 0 0 0  1  0  1  0  1 0 | 0 1 0 1 1
... ... ... xx.&#x  & |  2  2 |  0  0  1  2  0  0  1 |  *  *  * *  *  *  * 36  *  * * | 0 0 0 0  0  1  0  1  1 0 | 0 0 1 1 1
.x. ... .x. ...     & |  0  4 |  0  0  0  0  2  2  0 |  *  *  * *  *  *  *  * 18  * * | 0 0 0 0  1  0  1  0  0 1 | 0 1 0 1 1
.x. ... ... .x.     & |  0  4 |  0  0  0  0  2  0  2 |  *  *  * *  *  *  *  *  * 18 * | 0 0 0 0  0  1  0  1  0 1 | 0 0 1 1 1
... ... .x.3.x.       |  0  6 |  0  0  0  0  0  3  3 |  *  *  * *  *  *  *  *  *  * 6 | 0 0 0 0  0  0  0  0  2 2 | 0 0 0 2 2
----------------------+-------+----------------------+--------------------------------+--------------------------+----------
o..3x.. x.. ...     &   6  0 |  6  3  0  0  0  0  0 |  2  3  0 0  0  0  0  0  0  0 0 | 6 * * *  *  *  *  *  * * | 1 1 0 0 0
o..3x.. ... x..     &   6  0 |  6  0  3  0  0  0  0 |  2  0  3 0  0  0  0  0  0  0 0 | * 6 * *  *  *  *  *  * * | 1 0 1 0 0
... x.. x..3x..     &  12  0 |  6  6  6  0  0  0  0 |  0  3  3 2  0  0  0  0  0  0 0 | * * 6 *  *  *  *  *  * * | 1 0 0 0 1
oxx3xxo ... ...&#xt     6  6 |  6  0  0 12  6  0  0 |  2  0  0 0  6  6  0  0  0  0 0 | * * * 6  *  *  *  *  * * | 0 1 1 0 0
ox. ... xx. ...&#x  &   2  4 |  0  1  0  4  2  2  0 |  0  0  0 0  2  0  2  0  1  0 0 | * * * * 18  *  *  *  * * | 0 1 0 1 0
ox. ... ... xx.&#x  &   2  4 |  0  0  1  4  2  0  2 |  0  0  0 0  2  0  0  2  0  1 0 | * * * *  * 18  *  *  * * | 0 0 1 1 0
... xx. xx. ...&#x  &   4  4 |  2  2  0  4  2  2  0 |  0  1  0 0  0  2  2  0  1  0 0 | * * * *  *  * 18  *  * * | 0 1 0 0 1
... xx. ... xx.&#x  &   4  4 |  2  0  2  4  2  0  2 |  0  0  1 0  0  2  0  2  0  1 0 | * * * *  *  *  * 18  * * | 0 0 1 0 1
... ... xx.3xx.&#x  &   6  6 |  0  3  3  6  0  3  3 |  0  0  0 1  0  0  3  3  0  0 1 | * * * *  *  *  *  * 12 * | 0 0 0 1 1
.x. ... .x.3.x.     &   0 12 |  0  0  0  0  6  6  6 |  0  0  0 0  0  0  0  0  3  3 2 | * * * *  *  *  *  *  * 6 | 0 0 0 1 1
----------------------+-------+----------------------+--------------------------------+--------------------------+----------
o..3x.. x..3x..     &  18  0 | 18  9  9  0  0  0  0 |  6  9  9 3  0  0  0  0  0  0 0 | 3 3 3 0  0  0  0  0  0 0 | 2 * * * *
oxx3xxo xxx ...&#xt    12 12 | 12  6  0 24 12  6  0 |  4  6  0 0 12 12 12  0  6  0 0 | 2 0 0 2  6  0  6  0  0 0 | * 3 * * *
oxx3xxo ... xxx&#xt    12 12 | 12  0  6 24 12  0  6 |  4  0  6 0 12 12  0 12  0  6 0 | 0 2 0 2  0  6  0  6  0 0 | * * 3 * *
ox. ... xx.3xx.&#x  &   6 12 |  0  3  3 12  6  6  6 |  0  0  0 1  6  0  6  6  3  3 2 | 0 0 0 0  3  3  0  0  2 1 | * * * 6 *
... xx. xx.3xx.&#x  &  12 12 |  6  6  6 12  6  6  6 |  0  3  3 2  0  6  6  6  3  3 2 | 0 0 1 0  0  0  3  3  2 1 | * * * * 6

© 2004-2019
top of page