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

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