Acronym hiddip
Name hexagonal-hexagonal duoprism,
Voronoi cell of lattice A2×A2
  ©    
Circumradius sqrt(2) = 1.414214
Volume 27/4 = 6.75
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {6} between hip and hip:   120°
  • at {4} between hip and hip:   90°
Face vector 36, 72, 48, 12
Confer
general duoprisms:
6,n-dip   n,n-dip   n,m-dip   2n,m-dip   2n,2m-dip  
compounds:
affip   datap  
general polytopal classes:
Wythoffian polychora   noble polytopes   bistratic lace towers   lace simplices  
External
links
hedrondude   wikipedia   polytopewiki

It ought be emphasized that the 4-coloring, shown in the net above, represents hiddip's representation according to x3x x3x.

It further shall be pointed out that hiddip plays the role of the acceptance domain for the quasiperiodic Stampfli tiling.


Incidence matrix according to Dynkin symbol

x6o x6o

. . . . | 36 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 36  * | 1  2 0 | 2 1
. . x . |  2 |  * 36 | 0  2 1 | 1 2
--------+----+-------+--------+----
x6o . . |  6 |  6  0 | 6  * * | 2 0
x . x . |  4 |  2  2 | * 36 * | 1 1
. . x6o |  6 |  0  6 | *  * 6 | 0 2
--------+----+-------+--------+----
x6o x .  12 | 12  6 | 2  6 0 | 6 *
x . x6o  12 |  6 12 | 0  6 2 | * 6

snubbed forms: s6o2s6o
or
. . . .    | 36 |  4 |  2  4 |  4
-----------+----+----+-------+---
x . . .  & |  2 | 72 |  1  2 |  3
-----------+----+----+-------+---
x6o . .  & |  6 |  6 | 12  * |  2
x . x .    |  4 |  4 |  * 36 |  2
-----------+----+----+-------+---
x6o x .  &  12 | 18 |  2  6 | 12

x3x x6o

. . . . | 36 |  1  1  2 | 1  2  2 1 | 2 1 1
--------+----+----------+-----------+------
x . . . |  2 | 18  *  * | 1  2  0 0 | 2 1 0
. x . . |  2 |  * 18  * | 1  0  2 0 | 2 0 1
. . x . |  2 |  *  * 36 | 0  1  1 1 | 1 1 1
--------+----+----------+-----------+------
x3x . . |  6 |  3  3  0 | 6  *  * * | 2 0 0
x . x . |  4 |  2  0  2 | * 18  * * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 18 * | 1 0 1
. . x6o |  6 |  0  0  6 | *  *  * 6 | 0 1 1
--------+----+----------+-----------+------
x3x x .  12 |  6  6  6 | 2  3  3 0 | 6 * *
x . x6o  12 |  6  0 12 | 0  6  0 2 | * 3 *
. x x6o  12 |  0  6 12 | 0  0  6 2 | * * 3

x3x x3x

. . . . | 36 |  1  1  1  1 | 1 1 1 1 1 1 | 1 1 1 1
--------+----+-------------+-------------+--------
x . . . |  2 | 18  *  *  * | 1 1 1 0 0 0 | 1 1 1 0
. x . . |  2 |  * 18  *  * | 1 0 0 1 1 0 | 1 1 0 1
. . x . |  2 |  *  * 18  * | 0 1 0 1 0 1 | 1 0 1 1
. . . x |  2 |  *  *  * 18 | 0 0 1 0 1 1 | 0 1 1 1
--------+----+-------------+-------------+--------
x3x . . |  6 |  3  3  0  0 | 6 * * * * * | 1 1 0 0
x . x . |  4 |  2  0  2  0 | * 9 * * * * | 1 0 1 0
x . . x |  4 |  2  0  0  2 | * * 9 * * * | 0 1 1 0
. x x . |  4 |  0  2  2  0 | * * * 9 * * | 1 0 0 1
. x . x |  4 |  0  2  0  2 | * * * * 9 * | 0 1 0 1
. . x3x |  6 |  0  0  3  3 | * * * * * 6 | 0 0 1 1
--------+----+-------------+-------------+--------
x3x x .  12 |  6  6  6  0 | 2 3 0 3 0 0 | 3 * * *
x3x . x  12 |  6  6  0  6 | 2 0 3 0 3 0 | * 3 * *
x . x3x  12 |  6  0  6  6 | 0 3 3 0 0 2 | * * 3 *
. x x3x  12 |  0  6  6  6 | 0 0 0 3 3 2 | * * * 3

snubbed forms: s3s2x3x, s3s2s3s

xux xxx6ooo&#xt   → both heights = sqrt(3)/2 = 0.866025
(hip || pseudo (x,u)-hip || hip)

o.. o..6o..     | 12  *  * | 1  2  1  0  0 0  0 | 2 1  2 1 0  0 0 0 | 1 1 2 0 0
.o. .o.6.o.     |  * 12  * | 0  0  1  2  1 0  0 | 0 0  2 1 1  2 0 0 | 0 1 2 1 0
..o ..o6..o     |  *  * 12 | 0  0  0  0  1 1  2 | 0 0  0 1 0  2 2 1 | 0 0 2 1 1
----------------+----------+--------------------+-------------------+----------
x.. ... ...     |  2  0  0 | 6  *  *  *  * *  * | 2 0  0 1 0  0 0 0 | 1 0 2 0 0
... x.. ...     |  2  0  0 | * 12  *  *  * *  * | 1 1  1 0 0  0 0 0 | 1 1 1 0 0
oo. oo.6oo.&#x  |  1  1  0 | *  * 12  *  * *  * | 0 0  2 1 0  0 0 0 | 0 1 2 0 0
... .x. ...     |  0  2  0 | *  *  * 12  * *  * | 0 0  1 0 1  1 0 0 | 0 1 1 1 0
.oo .oo6.oo&#x  |  0  1  1 | *  *  *  * 12 *  * | 0 0  0 1 0  2 0 0 | 0 0 2 1 0
..x ... ...     |  0  0  2 | *  *  *  *  * 6  * | 0 0  0 1 0  0 2 0 | 0 0 2 0 1
... ..x ...     |  0  0  2 | *  *  *  *  * * 12 | 0 0  0 0 0  1 1 1 | 0 0 1 1 1
----------------+----------+--------------------+-------------------+----------
x.. x.. ...     |  4  0  0 | 2  2  0  0  0 0  0 | 6 *  * * *  * * * | 1 0 1 0 0
... x..6o..     |  6  0  0 | 0  6  0  0  0 0  0 | * 2  * * *  * * * | 1 1 0 0 0
... xx. ...&#x  |  2  2  0 | 0  1  2  1  0 0  0 | * * 12 * *  * * * | 0 1 1 0 0
xux ... ...&#xt |  2  2  2 | 1  0  2  0  2 1  0 | * *  * 6 *  * * * | 0 0 2 0 0
... .x.6.o.     |  0  6  0 | 0  0  0  6  0 0  0 | * *  * * 2  * * * | 0 1 0 1 0
... .xx ...&#x  |  0  2  2 | 0  0  0  1  2 0  1 | * *  * * * 12 * * | 0 0 1 1 0
..x ..x ...     |  0  0  4 | 0  0  0  0  0 2  2 | * *  * * *  * 6 * | 0 0 1 0 1
... ..x6..o     |  0  0  6 | 0  0  0  0  0 0  6 | * *  * * *  * * 2 | 0 0 0 1 1
----------------+----------+--------------------+-------------------+----------
x.. x..6o..      12  0  0 | 6 12  0  0  0 0  0 | 6 2  0 0 0  0 0 0 | 1 * * * *
... xx.6oo.&#x    6  6  0 | 0  6  6  6  0 0  0 | 0 1  6 0 1  0 0 0 | * 2 * * *
xux xxx ...&#xt   4  4  4 | 2  2  4  2  4 2  2 | 1 0  2 2 0  2 1 0 | * * 6 * *
... .xx6.oo&#x    0  6  6 | 0  0  0  6  6 0  6 | 0 0  0 0 1  6 0 1 | * * * 2 *
..x ..x6..o       0  0 12 | 0  0  0  0  0 6 12 | 0 0  0 0 0  0 6 2 | * * * * 1
or
o.. o..6o..      & | 24  * |  1  2  1  0 |  2 1  2 1 0 | 1 1 2
.o. .o.6.o.        |  * 12 |  0  0  2  2 |  0 0  4 1 1 | 0 2 2
-------------------+-------+-------------+-------------+------
x.. ... ...      & |  2  0 | 12  *  *  * |  2 0  0 1 0 | 1 0 2
... x.. ...      & |  2  0 |  * 24  *  * |  1 1  1 0 0 | 1 1 1
oo. oo.6oo.&#x   & |  1  1 |  *  * 24  * |  0 0  2 1 0 | 0 1 2
... .x. ...        |  0  2 |  *  *  * 12 |  0 0  2 0 1 | 0 2 1
-------------------+-------+-------------+-------------+------
x.. x.. ...      & |  4  0 |  2  2  0  0 | 12 *  * * * | 1 0 1
... x..6o..      & |  6  0 |  0  6  0  0 |  * 4  * * * | 1 1 0
... xx. ...&#x   & |  2  2 |  0  1  2  1 |  * * 24 * * | 0 1 1
xux ... ...&#xt    |  4  2 |  2  0  4  0 |  * *  * 6 * | 0 0 2
... .x.6.o.        |  0  6 |  0  0  0  6 |  * *  * * 2 | 0 2 0
-------------------+-------+-------------+-------------+------
x.. x..6o..      &  12  0 |  6 12  0  0 |  6 2  0 0 0 | 2 * *
... xx.6oo.&#x   &   6  6 |  0  6  6  6 |  0 1  6 0 1 | * 4 *
xux xxx ...&#xt      8  4 |  4  4  8  2 |  2 0  4 2 0 | * * 6

xux xxx3xxx&#xt   → both heights = sqrt(3)/2 = 0.866025
(hip || pseudo (x,u)-hip || hip)

o.. o..3o..     | 12  *  * | 1 1 1  1 0 0  0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0
.o. .o.3.o.     |  * 12  * | 0 0 0  1 1 1  1 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
..o ..o3..o     |  *  * 12 | 0 0 0  0 0 0  1 1 1 1 | 0 0 0 1 0 0 0 1 1 1 1 1 | 0 1 1 0 1 1
----------------+----------+-----------------------+-------------------------+------------
x.. ... ...     |  2  0  0 | 6 * *  * * *  * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... x.. ...     |  2  0  0 | * 6 *  * * *  * * * * | 1 0 1 0 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... x..     |  2  0  0 | * * 6  * * *  * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
oo. oo.3oo.&#x  |  1  1  0 | * * * 12 * *  * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
... .x. ...     |  0  2  0 | * * *  * 6 *  * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 | 0 1 0 1 1 0
... ... .x.     |  0  2  0 | * * *  * * 6  * * * * | 0 0 0 0 0 1 1 0 1 0 0 0 | 0 0 1 1 1 0
.oo .oo3.oo&#x  |  0  1  1 | * * *  * * * 12 * * * | 0 0 0 1 0 0 0 1 1 0 0 0 | 0 1 1 0 1 0
..x ... ...     |  0  0  2 | * * *  * * *  * 6 * * | 0 0 0 1 0 0 0 0 0 1 1 0 | 0 1 1 0 0 1
... ..x ...     |  0  0  2 | * * *  * * *  * * 6 * | 0 0 0 0 0 0 0 1 0 1 0 1 | 0 1 0 0 1 1
... ... ..x     |  0  0  2 | * * *  * * *  * * * 6 | 0 0 0 0 0 0 0 0 1 0 1 1 | 0 0 1 0 1 1
----------------+----------+-----------------------+-------------------------+------------
x.. x.. ...     |  4  0  0 | 2 2 0  0 0 0  0 0 0 0 | 3 * * * * * * * * * * * | 1 1 0 0 0 0
x.. ... x..     |  4  0  0 | 2 0 2  0 0 0  0 0 0 0 | * 3 * * * * * * * * * * | 1 0 1 0 0 0
... x..3x..     |  6  0  0 | 0 3 3  0 0 0  0 0 0 0 | * * 2 * * * * * * * * * | 1 0 0 1 0 0
xux ... ...&#xt |  2  2  2 | 1 0 0  2 0 0  2 1 0 0 | * * * 6 * * * * * * * * | 0 1 1 0 0 0
... xx. ...&#x  |  2  2  0 | 0 1 0  2 1 0  0 0 0 0 | * * * * 6 * * * * * * * | 0 1 0 1 0 0
... ... xx.&#x  |  2  2  0 | 0 0 1  2 0 1  0 0 0 0 | * * * * * 6 * * * * * * | 0 0 1 1 0 0
... .x.3.x.     |  0  6  0 | 0 0 0  0 3 3  0 0 0 0 | * * * * * * 2 * * * * * | 0 0 0 1 1 0
... .xx ...&#x  |  0  2  2 | 0 0 0  0 1 0  2 0 1 0 | * * * * * * * 6 * * * * | 0 1 0 0 1 0
... ... .xx&#x  |  0  2  2 | 0 0 0  0 0 1  2 0 0 1 | * * * * * * * * 6 * * * | 0 0 1 0 1 0
..x ..x ...     |  0  0  4 | 0 0 0  0 0 0  0 2 2 0 | * * * * * * * * * 3 * * | 0 1 0 0 0 1
..x ... ..x     |  0  0  4 | 0 0 0  0 0 0  0 2 0 2 | * * * * * * * * * * 3 * | 0 0 1 0 0 1
... ..x3..x     |  0  0  6 | 0 0 0  0 0 0  0 0 3 3 | * * * * * * * * * * * 2 | 0 0 0 0 1 1
----------------+----------+-----------------------+-------------------------+------------
x.. x..3x..      12  0  0 | 6 6 6  0 0 0  0 0 0 0 | 3 3 2 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xux xxx ...&#xt   4  4  4 | 2 2 0  4 2 0  4 2 2 0 | 1 0 0 2 2 0 0 2 0 1 0 0 | * 3 * * * *
xux ... xxx&#xt   4  4  4 | 2 0 2  4 0 2  4 2 0 2 | 0 1 0 2 0 2 0 0 2 0 1 0 | * * 3 * * *
... xx.3xx.&#x    6  6  0 | 0 3 3  6 3 3  0 0 0 0 | 0 0 1 0 3 3 1 0 0 0 0 0 | * * * 2 * *
... .xx3.xx&#x    0  6  6 | 0 0 0  0 3 3  6 0 3 3 | 0 0 0 0 0 0 1 3 3 0 0 1 | * * * * 2 *
..x ..x3..x       0  0 12 | 0 0 0  0 0 0  0 6 6 6 | 0 0 0 0 0 0 0 0 0 3 3 2 | * * * * * 1

© 2004-2024
top of page