Acronym hip
TOCID symbol (6)P, t(3)P
Name hexagonal prism,
Voronoi cell of unit-stacked hexagonal lattice
Circumradius sqrt(5)/2 = 1.118034
Vertex figure [42,6]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {4} and {4}:   120°
  • between {4} and {6}:   90°
Confer
general prisms:
n-p   n/d-p   2n-p.  
variations:
u x6o   pacop  
compounds:
griso   rosi  
general polytopal classes:
segmentohedra   bistratic lace towers  
External
links
wikipedia   WikiChoron   mathworld   quickfur

Incidence matrix according to Dynkin symbol

x x6o

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

snubbed forms: s2s6o

x x3x

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

snubbed forms: x2β3x, β2β3x, x2s3s, s2s3s

x2s12o

demi( . .  . ) | 12 | 1  2 | 1 2
---------------+----+------+----
demi( x .  . ) |  2 | 6  * | 0 2
sefa( . s12o ) |  2 | * 12 | 1 1
---------------+----+------+----
      . s12o   |  6 | 0  6 | 2 *
sefa( x2s12o ) |  4 | 2  2 | * 6

starting figure: x x12o

x2s6s

demi( . . . ) | 12 | 1  2 | 1 2
--------------+----+------+----
demi( x . . ) |  2 | 6  * | 0 2
sefa( . s6s ) |  2 | * 12 | 1 1
--------------+----+------+----
      . s6s   |  6 | 0  6 | 2 *
sefa( x2s6s ) |  4 | 2  2 | * 6

starting figure: x x6x

xx6oo&#x   → height = 1
({6} || {6})

o.6o.    | 6 * | 2 1 0 | 1 2 0
.o6.o    | * 6 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 6 * * | 1 1 0
oo6oo&#x | 1 1 | * 6 * | 0 2 0
.x ..    | 0 2 | * * 6 | 0 1 1
---------+-----+-------+------
x.6o.    | 6 0 | 6 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * 6 *
.x6.o    | 0 6 | 0 0 6 | * * 1

xx3xx&#x   → height = 1
({6} || {6})

o.3o.    | 6 * | 1 1 1 0 0 | 1 1 1 0
.o3.o    | * 6 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
x. ..    | 2 0 | 3 * * * * | 1 1 0 0
.. x.    | 2 0 | * 3 * * * | 1 0 1 0
oo3oo&#x | 1 1 | * * 6 * * | 0 1 1 0
.x ..    | 0 2 | * * * 3 * | 0 1 0 1
.. .x    | 0 2 | * * * * 3 | 0 0 1 1
---------+-----+-----------+--------
x.3x.    | 6 0 | 3 3 0 0 0 | 1 * * *
xx ..&#x | 2 2 | 1 0 2 1 0 | * 3 * *
.. xx&#x | 2 2 | 0 1 2 0 1 | * * 3 *
.x3.x    | 0 6 | 0 0 0 3 3 | * * * 1

xux xxx&#amp;xt   → both heights = sqrt(3)/2 = 0.866025
({4} || pseudo (u,x)-{4} || {4})

o.. o..     | 4 * * | 1 1 1 0 0 0 0 | 1 1 1 0 0
.o. .o.     | * 4 * | 0 0 1 1 1 0 0 | 0 1 1 1 0
..o ..o     | * * 4 | 0 0 0 0 1 1 1 | 0 0 1 1 1
------------+-------+---------------+----------
x.. ...     | 2 0 0 | 2 * * * * * * | 1 0 1 0 0
... x..     | 2 0 0 | * 2 * * * * * | 1 1 0 0 0
oo. oo.&#x  | 1 1 0 | * * 4 * * * * | 0 1 1 0 0
... .x.     | 0 2 0 | * * * 2 * * * | 0 1 0 1 0
.oo .oo&#x  | 0 1 1 | * * * * 4 * * | 0 0 1 1 0
..x ...     | 0 0 2 | * * * * * 2 * | 0 0 1 0 1
... ..x     | 0 0 2 | * * * * * * 2 | 0 0 0 1 1
------------+-------+---------------+----------
x.. x..     | 4 0 0 | 2 2 0 0 0 0 0 | 1 * * * *
... xx.&#x  | 2 2 0 | 0 1 2 1 0 0 0 | * 2 * * *
xux ...&#xt | 2 2 2 | 1 0 2 0 2 1 0 | * * 2 * *
... .xx&#x  | 0 2 2 | 0 0 0 1 2 0 1 | * * * 2 *
..x ..x     | 0 0 4 | 0 0 0 0 0 2 2 | * * * * 1
or
o.. o..      & | 8 * | 1 1 1 0 | 1 1 1
.o. .o.        | * 4 | 0 0 2 1 | 0 2 1
---------------+-----+---------+------
x.. ...      & | 2 0 | 4 * * * | 1 0 1
... x..      & | 2 0 | * 4 * * | 1 1 0
oo. oo.&#x   & | 1 1 | * * 8 * | 0 1 1
... .x.        | 0 2 | * * * 2 | 0 2 0
---------------+-----+---------+------
x.. x..      & | 4 0 | 2 2 0 0 | 2 * *
... xx.&#x   & | 2 2 | 0 1 2 1 | * 4 *
xux ...&#xt    | 4 2 | 2 0 4 0 | * * 2

xxxx ohho&#xt   → outer heights = 1/2
                  inner height = 1
(line || pseudo (x,h)-{4} || pseudo (x,h)-{4} || line)

o... o...     | 2 * * * | 1 2 0 0 0 0 0 | 2 1 0 0
.o.. .o..     | * 4 * * | 0 1 1 1 0 0 0 | 1 1 1 0
..o. ..o.     | * * 4 * | 0 0 0 1 1 1 0 | 0 1 1 1
...o ...o     | * * * 2 | 0 0 0 0 0 2 1 | 0 1 0 2
--------------+---------+---------------+--------
x... ....     | 2 0 0 0 | 1 * * * * * * | 2 0 0 0
oo.. oo..&#x  | 1 1 0 0 | * 4 * * * * * | 1 1 0 0
.x.. ....     | 0 2 0 0 | * * 2 * * * * | 1 0 1 0
.oo. .oo.&#x  | 0 1 1 0 | * * * 4 * * * | 0 1 1 0
..x. ....     | 0 0 2 0 | * * * * 2 * * | 0 0 1 1
..oo ..oo&#x  | 0 0 1 1 | * * * * * 4 * | 0 1 0 1
...x ....     | 0 0 0 2 | * * * * * * 1 | 0 0 0 2
--------------+---------+---------------+--------
xx.. ....&#x  | 2 2 0 0 | 1 2 1 0 0 0 0 | 2 * * *
.... ohho&#xt | 1 2 2 1 | 0 2 0 2 0 2 0 | * 2 * *
.xx. ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 0 | * * 2 *
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 1 2 1 | * * * 2
or
o... o...     & | 4 * | 1 2 0 0 | 2 1 0
.o.. .o..     & | * 8 | 0 1 1 1 | 1 1 1
----------------+-----+---------+------
x... ....     & | 2 0 | 2 * * * | 2 0 0
oo.. oo..&#x  & | 1 1 | * 8 * * | 1 1 0
.x.. ....     & | 0 2 | * * 4 * | 1 0 1
.oo. .oo.&#x    | 0 2 | * * * 4 | 0 1 1
----------------+-----+---------+------
xx.. ....&#x  & | 2 2 | 1 2 1 0 | 4 * *
.... ohho&#xt   | 2 4 | 0 4 0 2 | * 2 *
.xx. ....&#x    | 0 4 | 0 0 2 2 | * * 2

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