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] |
Volume | 3 sqrt(3)/2 = 2.598076 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
|
Dual | m2m6o |
Face vector | 12, 18, 8 |
Confer |
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External links |
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, s2s3s (as mere faceting)
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
s2s6x demi( . . . ) | 12 | 1 1 1 | 1 2 --------------+----+-------+---- demi( . . x ) | 2 | 6 * * | 1 1 s2s . | 2 | * 6 * | 0 2 sefa( . s6x ) | 2 | * * 6 | 1 1 --------------+----+-------+---- . s6x | 6 | 3 0 3 | 2 * sefa( s2s6x ) | 6 | 1 2 1 | * 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&#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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