Acronym | grich |
Name |
great rhombated cubic honeycomb, cantitruncated cubic honeycomb |
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Vertex figure |
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Confer |
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External links |
As abstract polytope grich is isomorphic to gaqrich, thereby replacing octagons by octagrams, resp. girco by quitco.
Incidence matrix according to Dynkin symbol
x4x3x4o (N → ∞) . . . . | 24N | 1 1 2 | 1 2 2 1 | 2 1 1 --------+-----+-------------+--------------+------- x . . . | 2 | 12N * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 12N * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 24N | 0 1 1 1 | 1 1 1 --------+-----+-------------+--------------+------- x4x . . | 8 | 4 4 0 | 3N * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 12N * * | 1 1 0 . x3x . | 6 | 0 3 3 | * * 8N * | 1 0 1 . . x4o | 4 | 0 0 4 | * * * 6N | 0 1 1 --------+-----+-------------+--------------+------- x4x3x . ♦ 48 | 24 24 24 | 6 12 8 0 | N * * x . x4o ♦ 8 | 4 0 8 | 0 4 0 2 | * 3N * . x3x4o ♦ 24 | 0 12 24 | 0 0 8 6 | * * N snubbed forms: s4x3x4o, x4s3s4o, s4s3s4o
x4x3x4/3o (N → ∞) . . . . | 24N | 1 1 2 | 1 2 2 1 | 2 1 1 ----------+-----+-------------+--------------+------- x . . . | 2 | 12N * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 12N * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 24N | 0 1 1 1 | 1 1 1 ----------+-----+-------------+--------------+------- x4x . . | 8 | 4 4 0 | 3N * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 12N * * | 1 1 0 . x3x . | 6 | 0 3 3 | * * 8N * | 1 0 1 . . x4/3o | 4 | 0 0 4 | * * * 6N | 0 1 1 ----------+-----+-------------+--------------+------- x4x3x . ♦ 48 | 24 24 24 | 6 12 8 0 | N * * x . x4/3o ♦ 8 | 4 0 8 | 0 4 0 2 | * 3N * . x3x4/3o ♦ 24 | 0 12 24 | 0 0 8 6 | * * N
x3x3x *b4x (N → ∞) . . . . | 48N | 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 -----------+-----+-----------------+----------------------+---------- x . . . | 2 | 24N * * * | 1 1 1 0 0 0 | 1 1 1 0 . x . . | 2 | * 24N * * | 1 0 0 1 1 0 | 1 1 0 1 . . x . | 2 | * * 24N * | 0 1 0 1 0 1 | 1 0 1 1 . . . x | 2 | * * * 24N | 0 0 1 0 1 1 | 0 1 1 1 -----------+-----+-----------------+----------------------+---------- x3x . . | 6 | 3 3 0 0 | 8N * * * * * | 1 1 0 0 x . x . | 4 | 2 0 2 0 | * 12N * * * * | 1 0 1 0 x . . x | 4 | 2 0 0 2 | * * 12N * * * | 0 1 1 0 . x3x . | 6 | 0 3 3 0 | * * * 8N * * | 1 0 0 1 . x . *b4x | 8 | 0 4 0 4 | * * * * 6N * | 0 1 0 1 . . x x | 4 | 0 0 2 2 | * * * * * 12N | 0 0 1 1 -----------+-----+-----------------+----------------------+---------- x3x3x . ♦ 24 | 12 12 12 0 | 4 6 0 4 0 0 | 2N * * * x3x . *b4x ♦ 48 | 24 24 0 24 | 8 0 12 0 6 0 | * N * * x . x x ♦ 8 | 4 0 4 4 | 0 2 2 0 0 2 | * * 6N * . x3x *b4x ♦ 48 | 0 24 24 24 | 0 0 0 8 6 12 | * * * N snubbed forms: s3s3s *b4x, s3s3s *b4s
s4x3x4x (N → ∞) demi( . . . . ) | 48N | 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 ----------------+-----+-----------------+----------------------+---------- demi( . x . . ) | 2 | 24N * * * | 1 1 0 1 0 0 | 1 1 1 0 demi( . . x . ) | 2 | * 24N * * | 1 0 1 0 1 0 | 1 1 0 1 demi( . . . x ) | 2 | * * 24N * | 0 1 1 0 0 1 | 1 0 1 1 sefa( s4x . . ) | 2 | * * * 24N | 0 0 0 1 1 1 | 0 1 1 1 ----------------+-----+-----------------+----------------------+---------- demi( . x3x . ) | 6 | 3 3 0 0 | 8N * * * * * | 1 1 0 0 demi( . x . x ) | 4 | 2 0 2 0 | * 12N * * * * | 1 0 1 0 demi( . . x4x ) | 8 | 0 4 4 0 | * * 6N * * * | 1 0 0 1 s4x . . | 4 | 2 0 0 2 | * * * 12N * * | 0 1 1 0 sefa( s4x3x . ) | 6 | 0 3 0 3 | * * * * 8N * | 0 1 0 1 sefa( s4x . x ) | 4 | 0 0 2 2 | * * * * * 12N | 0 0 1 1 ----------------+-----+-----------------+----------------------+---------- demi( . x3x4x ) ♦ 48 | 24 24 24 0 | 8 12 6 0 0 0 | N * * * s4x3x . ♦ 24 | 12 12 0 12 | 4 0 0 6 4 0 | * 2N * * s4x . x ♦ 8 | 4 0 4 4 | 0 2 0 2 0 2 | * * 6N * sefa( s4x3x4x ) ♦ 48 | 0 24 24 24 | 0 0 6 0 8 12 | * * * N starting figure: x4x3x4x
:wxxxw:4:xuxux:4:ooqoo:&##x (N → ∞) → height(1,2) = height(2,3) = height(3,4) = height(4,5) = 1/sqrt(2) = 0.707107 height(5,1') = 1 o.... 4 o.... 4 o.... | 4N * * * * | 2 1 0 0 0 0 0 0 0 0 1 | 1 2 0 0 0 0 0 0 1 2 | 1 0 2 1 .o... 4 .o... 4 .o... | * 4N * * * | 0 1 1 2 0 0 0 0 0 0 0 | 0 2 2 1 0 0 0 0 1 0 | 1 1 2 0 ..o.. 4 ..o.. 4 ..o.. | * * 8N * * | 0 0 0 1 1 1 1 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 2 0 ...o. 4 ...o. 4 ...o. | * * * 4N * | 0 0 0 0 0 0 2 1 1 0 0 | 0 0 0 1 0 2 2 0 1 0 | 1 1 2 0 ....o 4 ....o 4 ....o | * * * * 4N | 0 0 0 0 0 0 0 0 1 2 1 | 0 0 0 0 0 0 2 1 1 2 | 1 0 2 1 ----------------------------+----------------+----------------------------------+----------------------------+--------- ..... x.... ..... | 2 0 0 0 0 | 4N * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 1 | 1 0 1 1 oo... 4 oo... 4 oo... &#x | 1 1 0 0 0 | * 4N * * * * * * * * * | 0 2 0 0 0 0 0 0 1 0 | 1 0 2 0 .x... ..... ..... | 0 2 0 0 0 | * * 2N * * * * * * * * | 0 0 2 0 0 0 0 0 1 0 | 0 1 2 0 .oo.. 4 .oo.. 4 .oo.. &#x | 0 1 1 0 0 | * * * 8N * * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 ..x.. ..... ..... | 0 0 2 0 0 | * * * * 4N * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 2 0 ..... ..x.. ..... | 0 0 2 0 0 | * * * * * 4N * * * * * | 0 1 0 0 1 0 1 0 0 0 | 1 0 2 0 ..oo. 4 ..oo. 4 ..oo. &#x | 0 0 1 1 0 | * * * * * * 8N * * * * | 0 0 0 1 0 1 1 0 0 0 | 1 1 1 0 ...x. ..... ..... | 0 0 0 2 0 | * * * * * * * 2N * * * | 0 0 0 0 0 2 0 0 1 0 | 0 1 2 0 ...oo 4 ...oo 4 ...oo &#x | 0 0 0 1 1 | * * * * * * * * 4N * * | 0 0 0 0 0 0 2 0 1 0 | 1 0 2 0 ..... ....x ..... | 0 0 0 0 2 | * * * * * * * * * 4N * | 0 0 0 0 0 0 1 1 0 1 | 1 0 1 1 :o...o:4:o...o:4:o...o:&#x | 1 0 0 0 1 | * * * * * * * * * * 4N | 0 0 0 0 0 0 0 0 1 2 | 0 0 2 1 ----------------------------+----------------+----------------------------------+----------------------------+--------- ..... x.... 4 o.... | 4 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | N * * * * * * * * * | 1 0 0 1 ..... xux.. ..... &#xt | 2 2 2 0 0 | 1 2 0 2 0 1 0 0 0 0 0 | * 4N * * * * * * * * | 1 0 1 0 .xx.. ..... ..... &#x | 0 2 2 0 0 | 0 0 1 2 1 0 0 0 0 0 0 | * * 4N * * * * * * * | 0 1 1 0 ..... ..... .oqo. &#xt | 0 1 2 1 0 | 0 0 0 2 0 0 2 0 0 0 0 | * * * 4N * * * * * * | 1 1 0 0 ..x.. 4 ..x.. ..... | 0 0 8 0 0 | 0 0 0 0 4 4 0 0 0 0 0 | * * * * N * * * * * | 0 0 2 0 ..xx. ..... ..... &#x | 0 0 2 2 0 | 0 0 0 0 1 0 2 1 0 0 0 | * * * * * 4N * * * * | 0 1 1 0 ..... ..xux ..... &#xt | 0 0 2 2 2 | 0 0 0 0 0 1 2 0 2 1 0 | * * * * * * 4N * * * | 1 0 1 0 ..... ....x 4 ....o | 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 4 0 | * * * * * * * N * * | 1 0 0 1 :wx.xw: ..... ..... &#xt | 2 2 0 2 2 | 0 2 1 0 0 0 0 1 2 0 2 | * * * * * * * * 2N * | 0 0 2 0 ..... :x...x: ..... &#x | 2 0 0 0 2 | 1 0 0 0 0 0 0 0 0 1 2 | * * * * * * * * * 4N | 0 0 1 1 ----------------------------+----------------+----------------------------------+----------------------------+--------- ..... xuxux 4 ooqoo &#xt ♦ 4 4 8 4 4 | 4 4 0 8 0 4 8 0 4 4 0 | 1 4 0 4 0 0 4 1 0 0 | N * * * .xxx. ..... .oqo. &#xt ♦ 0 2 4 2 0 | 0 0 1 4 2 0 4 1 0 0 0 | 0 0 2 2 0 2 0 0 0 0 | * 2N * * :wxxxw:4:xuxux: ..... &#xt ♦ 8 8 16 8 8 | 4 8 4 8 8 8 8 4 8 4 8 | 0 4 4 0 2 4 4 0 4 4 | * * N * ..... :x...x:4:o...o:&#x ♦ 4 0 0 0 4 | 4 0 0 0 0 0 0 0 0 4 4 | 1 0 0 0 0 0 0 1 0 4 | * * * N
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