Acronym | sarx | |||||||||||||||||||||||||||||||||||||||||||||
Name |
small rhombated hexateron, cantellated hexateron | |||||||||||||||||||||||||||||||||||||||||||||
Circumradius | sqrt(5/3) = 1.290994 | |||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Lace city in approx. ASCII-art |
x3o3o o3x3o -- o3x3o3o (rap) x3o3o u3o3o x3x3o -- x3x3o3o (tip) o3x3o x3x3o x3o3x -- x3o3x3o (srip) | |||||||||||||||||||||||||||||||||||||||||||||
Lace hyper city in approx. ASCII-art |
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General of army | (is itself convex) | |||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polyteral members:
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Dihedral angles
(at margins) | ||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 60, 240, 290, 135, 27 | |||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x3o3x3o3o . . . . . | 60 | 2 6 | 1 6 3 6 | 3 6 3 2 | 3 2 1 ----------+----+--------+--------------+-------------+------- x . . . . | 2 | 60 * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . . x . . | 2 | * 180 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+--------+--------------+-------------+------- x3o . . . | 3 | 3 0 | 20 * * * | 3 0 0 0 | 3 0 0 x . x . . | 4 | 2 2 | * 90 * * | 1 2 0 0 | 2 1 0 . o3x . . | 3 | 0 3 | * * 60 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 3 | * * * 120 | 0 1 1 1 | 1 1 1 ----------+----+--------+--------------+-------------+------- x3o3x . . ♦ 12 | 12 12 | 4 6 4 0 | 15 * * * | 2 0 0 x . x3o . ♦ 6 | 3 6 | 0 3 0 2 | * 60 * * | 1 1 0 . o3x3o . ♦ 6 | 0 12 | 0 0 4 4 | * * 30 * | 1 0 1 . . x3o3o ♦ 4 | 0 6 | 0 0 0 4 | * * * 30 | 0 1 1 ----------+----+--------+--------------+-------------+------- x3o3x3o . ♦ 30 | 30 60 | 10 30 20 20 | 5 10 5 0 | 6 * * x . x3o3o ♦ 8 | 4 12 | 0 6 0 8 | 0 4 0 2 | * 15 * . o3x3o3o ♦ 10 | 0 30 | 0 0 10 20 | 0 0 5 5 | * * 6
x3o3x3o3/2o . . . . . | 60 | 2 6 | 1 6 3 6 | 3 6 3 2 | 3 2 1 ------------+----+--------+--------------+-------------+------- x . . . . | 2 | 60 * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . . x . . | 2 | * 180 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ------------+----+--------+--------------+-------------+------- x3o . . . | 3 | 3 0 | 20 * * * | 3 0 0 0 | 3 0 0 x . x . . | 4 | 2 2 | * 90 * * | 1 2 0 0 | 2 1 0 . o3x . . | 3 | 0 3 | * * 60 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 3 | * * * 120 | 0 1 1 1 | 1 1 1 ------------+----+--------+--------------+-------------+------- x3o3x . . ♦ 12 | 12 12 | 4 6 4 0 | 15 * * * | 2 0 0 x . x3o . ♦ 6 | 3 6 | 0 3 0 2 | * 60 * * | 1 1 0 . o3x3o . ♦ 6 | 0 12 | 0 0 4 4 | * * 30 * | 1 0 1 . . x3o3/2o ♦ 4 | 0 6 | 0 0 0 4 | * * * 30 | 0 1 1 ------------+----+--------+--------------+-------------+------- x3o3x3o . ♦ 30 | 30 60 | 10 30 20 20 | 5 10 5 0 | 6 * * x . x3o3/2o ♦ 8 | 4 12 | 0 6 0 8 | 0 4 0 2 | * 15 * . o3x3o3/2o ♦ 10 | 0 30 | 0 0 10 20 | 0 0 5 5 | * * 6
oxx3xxo3oox3ooo&#xt → both heights = sqrt(3/5) = 0.774597 (rap || pseudo tip || srip) o..3o..3o..3o.. | 10 * * | 6 2 0 0 0 0 0 | 3 6 1 6 0 0 0 0 0 0 0 0 | 3 2 6 3 0 0 0 0 0 0 0 | 1 2 3 0 0 0 .o.3.o.3.o.3.o. | * 20 * | 0 1 1 3 3 0 0 | 0 0 1 3 3 3 3 3 0 0 0 0 | 0 0 3 3 1 3 3 1 0 0 0 | 0 1 3 1 1 0 ..o3..o3..o3..o | * * 30 | 0 0 0 0 2 2 4 | 0 0 0 0 0 2 1 4 1 4 2 2 | 0 0 0 1 0 4 2 2 2 2 1 | 0 0 2 2 1 1 --------------------+----------+----------------------+-------------------------------------+-----------------------------+------------- ... x.. ... ... | 2 0 0 | 30 * * * * * * | 1 2 0 1 0 0 0 0 0 0 0 0 | 2 1 2 1 0 0 0 0 0 0 0 | 1 1 2 0 0 0 oo.3oo.3oo.3oo.&#x | 1 1 0 | * 20 * * * * * | 0 0 1 3 0 0 0 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 0 0 | 0 1 3 0 0 0 .x. ... ... ... | 0 2 0 | * * 10 * * * * | 0 0 1 0 0 3 0 0 0 0 0 0 | 0 0 0 3 0 3 0 0 0 0 0 | 0 0 3 1 0 0 ... .x. ... ... | 0 2 0 | * * * 30 * * * | 0 0 0 1 2 0 1 0 0 0 0 0 | 0 0 2 1 1 0 2 0 0 0 0 | 0 1 2 0 1 0 .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * * 60 * * | 0 0 0 0 0 1 1 2 0 0 0 0 | 0 0 0 1 0 2 2 1 0 0 0 | 0 0 2 1 1 0 ..x ... ... ... | 0 0 2 | * * * * * 30 * | 0 0 0 0 0 1 0 0 1 2 0 0 | 0 0 0 1 0 2 0 0 2 1 0 | 0 0 2 1 0 1 ... ... ..x ... | 0 0 2 | * * * * * * 60 | 0 0 0 0 0 0 0 1 0 1 1 1 | 0 0 0 0 0 1 1 1 1 1 1 | 0 0 1 1 1 1 --------------------+----------+----------------------+-------------------------------------+-----------------------------+------------- o..3x.. ... ... | 3 0 0 | 3 0 0 0 0 0 0 | 10 * * * * * * * * * * * | 2 0 0 1 0 0 0 0 0 0 0 | 1 0 2 0 0 0 ... x..3o.. ... | 3 0 0 | 3 0 0 0 0 0 0 | * 20 * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 ox. ... ... ...&#x | 1 2 0 | 0 2 1 0 0 0 0 | * * 10 * * * * * * * * * | 0 0 0 3 0 0 0 0 0 0 0 | 0 0 3 0 0 0 ... xx. ... ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * * * 30 * * * * * * * * | 0 0 2 1 0 0 0 0 0 0 0 | 0 1 2 0 0 0 ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 0 | * * * * 20 * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 | 0 1 1 0 1 0 .xx ... ... ...&#x | 0 2 2 | 0 0 1 0 2 1 0 | * * * * * 30 * * * * * * | 0 0 0 1 0 2 0 0 0 0 0 | 0 0 2 1 0 0 ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 0 0 | * * * * * * 30 * * * * * | 0 0 0 1 0 0 2 0 0 0 0 | 0 0 2 0 1 0 ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 2 0 1 | * * * * * * * 60 * * * * | 0 0 0 0 0 1 1 1 0 0 0 | 0 0 1 1 1 0 ..x3..o ... ... | 0 0 3 | 0 0 0 0 0 3 0 | * * * * * * * * 10 * * * | 0 0 0 1 0 0 0 0 2 0 0 | 0 0 2 0 0 1 ..x ... ..x ... | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * * 30 * * | 0 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 0 1 ... ..o3..x ... | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * 20 * | 0 0 0 0 0 0 1 0 1 0 1 | 0 0 1 0 1 1 ... ... ..x3..o | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * * 20 | 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1 --------------------+----------+----------------------+-------------------------------------+-----------------------------+------------- o..3x..3o.. ... ♦ 6 0 0 | 12 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 | 5 * * * * * * * * * * | 1 0 1 0 0 0 ... x..3o..3o.. ♦ 4 0 0 | 6 0 0 0 0 0 0 | 0 4 0 0 0 0 0 0 0 0 0 0 | * 5 * * * * * * * * * | 1 1 0 0 0 0 ... xx.3oo. ...&#x ♦ 3 3 0 | 3 3 0 3 0 0 0 | 0 1 0 3 1 0 0 0 0 0 0 0 | * * 20 * * * * * * * * | 0 1 1 0 0 0 oxx3xxo ... ...&#xt ♦ 3 6 3 | 3 6 3 3 6 3 0 | 1 0 3 3 0 3 3 0 1 0 0 0 | * * * 10 * * * * * * * | 0 0 2 0 0 0 ... .x.3.o.3.o. ♦ 0 4 0 | 0 0 0 6 0 0 0 | 0 0 0 0 4 0 0 0 0 0 0 0 | * * * * 5 * * * * * * | 0 1 0 0 1 0 .xx ... .ox ...&#x ♦ 0 2 4 | 0 0 1 0 4 2 2 | 0 0 0 0 0 2 0 2 0 1 0 0 | * * * * * 30 * * * * * | 0 0 1 1 0 0 ... .xo3.ox ...&#x ♦ 0 3 3 | 0 0 0 3 6 0 3 | 0 0 0 0 1 0 3 3 0 0 1 0 | * * * * * * 20 * * * * | 0 0 1 0 1 0 ... ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 0 3 0 3 | 0 0 0 0 0 0 0 3 0 0 0 1 | * * * * * * * 20 * * * | 0 0 0 1 1 0 ..x3..o3..x ... ♦ 0 0 12 | 0 0 0 0 0 12 12 | 0 0 0 0 0 0 0 0 4 6 4 0 | * * * * * * * * 5 * * | 0 0 1 0 0 1 ..x ... ..x3..o ♦ 0 0 6 | 0 0 0 0 0 3 6 | 0 0 0 0 0 0 0 0 0 3 0 2 | * * * * * * * * * 10 * | 0 0 0 1 0 1 ... ..o3..x3..o ♦ 0 0 6 | 0 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * 5 | 0 0 0 0 1 1 --------------------+----------+----------------------+-------------------------------------+-----------------------------+------------- o..3x..3o..3o.. ♦ 10 0 0 | 30 0 0 0 0 0 0 | 10 20 0 0 0 0 0 0 0 0 0 0 | 5 5 0 0 0 0 0 0 0 0 0 | 1 * * * * * ... xx.3oo.3oo.&#x ♦ 4 4 0 | 6 4 0 6 0 0 0 | 0 4 0 6 4 0 0 0 0 0 0 0 | 0 1 4 0 1 0 0 0 0 0 0 | * 5 * * * * oxx3xxo3oox ...&#xt ♦ 6 12 12 | 12 12 6 12 24 12 12 | 4 4 6 12 4 12 12 12 4 6 4 0 | 1 0 4 4 0 6 4 0 1 0 0 | * * 5 * * * .xx ... .ox3.oo&#x ♦ 0 2 6 | 0 0 1 0 6 3 6 | 0 0 0 0 0 3 0 6 0 3 0 2 | 0 0 0 0 0 3 0 2 0 1 0 | * * * 10 * * ... .xo3.ox3.oo&#x ♦ 0 4 6 | 0 0 0 6 12 0 12 | 0 0 0 0 4 0 6 12 0 0 4 4 | 0 0 0 0 1 0 4 4 0 0 1 | * * * * 5 * ..x3..o3..x3..o ♦ 0 0 30 | 0 0 0 0 0 30 60 | 0 0 0 0 0 0 0 0 10 30 20 20 | 0 0 0 0 0 0 0 0 5 10 5 | * * * * * 1
ox(ou)xx3oo(xo)xo xx(uo)xo3ox(ox)oo&#xt → all heights = 1/sqrt(3) = 0.577350 ({3} || pseudo thiddip || pseudo tegum sum of 2 alternate (x,u)-triddips || pseudo alternate thiddip || ortho {3}) o.(..)..3o.(..).. o.(..)..3o.(..).. & | 6 * * | 2 6 0 0 0 0 0 0 | 1 6 6 3 0 0 0 0 0 0 0 0 0 | 2 6 3 3 0 0 0 0 0 | 2 1 3 0 .o(..)..3.o(..).. .o(..)..3.o(..).. & | * 36 * | 0 1 2 1 1 2 1 0 | 0 2 1 1 1 2 2 1 2 2 1 1 0 | 1 2 2 1 1 1 1 2 3 | 1 1 3 1 ..(o.)..3..(o.).. ..(o.)..3..(o.).. & | * * 18 | 0 0 0 0 0 4 2 2 | 0 0 0 0 0 0 2 4 2 4 1 2 1 | 0 0 1 1 0 2 2 2 6 | 0 1 3 2 ------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+-------- ..(..).. ..(..).. x.(..).. ..(..).. & | 2 0 0 | 6 * * * * * * * | 1 0 3 0 0 0 0 0 0 0 0 0 0 | 0 3 0 3 0 0 0 0 0 | 1 0 3 0 oo(..)..3oo(..).. oo(..)..3oo(..)..&#x & | 1 1 0 | * 36 * * * * * * | 0 2 1 1 0 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 | 1 1 2 0 .x(..).. ..(..).. ..(..).. ..(..).. & | 0 2 0 | * * 36 * * * * * | 0 1 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 1 1 0 1 0 | 1 1 2 0 ..(..).. ..(..).. .x(..).. ..(..).. & | 0 2 0 | * * * 18 * * * * | 0 0 1 0 0 2 0 0 0 0 1 0 0 | 0 2 0 1 1 0 0 2 0 | 1 0 3 0 ..(..).. ..(..).. ..(..).. .x(..).. & | 0 2 0 | * * * * 18 * * * | 0 0 0 1 0 0 0 0 2 0 0 1 0 | 0 0 2 1 0 0 1 0 2 | 0 1 2 1 .o(o.)..3.o(o.).. .o(o.)..3.o(o.)..&#x & | 0 1 1 | * * * * * 72 * * | 0 0 0 0 0 0 1 1 1 1 0 0 0 | 0 0 1 0 0 1 1 1 2 | 0 1 2 1 .o(.o)..3.o(.o).. .o(.o)..3.o(.o)..&#x & | 0 1 1 | * * * * * * 36 * | 0 0 0 0 0 0 0 0 0 2 1 1 0 | 0 0 0 1 0 0 0 2 3 | 0 0 3 1 ..(..).. ..(x.).. ..(..).. ..(..).. & | 0 0 2 | * * * * * * * 18 | 0 0 0 0 0 0 0 2 0 0 0 1 1 | 0 0 0 1 0 2 1 0 2 | 0 1 2 1 ------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+-------- ..(..).. ..(..).. x.(..)..3..(o.).. & | 3 0 0 | 3 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 0 0 0 3 0 0 0 0 0 | 0 0 3 0 ox(..).. ..(..).. ..(..).. ..(..)..&#x & | 1 2 0 | 0 2 1 0 0 0 0 0 | * 36 * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 ..(..).. ..(..).. xx(..).. ..(..)..&#x & | 2 2 0 | 1 2 0 1 0 0 0 0 | * * 18 * * * * * * * * * * | 0 2 0 1 0 0 0 0 0 | 1 0 2 0 ..(..).. ..(..).. ..(..).. ox(..)..&#x & | 1 2 0 | 0 2 0 0 1 0 0 0 | * * * 18 * * * * * * * * * | 0 0 2 1 0 0 0 0 0 | 0 1 2 0 .x(..)..3.o(..).. ..(..).. ..(..).. & | 0 3 0 | 0 0 3 0 0 0 0 0 | * * * * 12 * * * * * * * * | 1 0 0 0 1 1 0 0 0 | 1 1 1 0 .x(..).. ..(..).. .x(..).. ..(..).. & | 0 4 0 | 0 0 2 2 0 0 0 0 | * * * * * 18 * * * * * * * | 0 1 0 0 1 0 0 1 0 | 1 0 2 0 .x(o.).. ..(..).. ..(..).. ..(..)..&#x & | 0 2 1 | 0 0 1 0 0 2 0 0 | * * * * * * 36 * * * * * * | 0 0 1 0 0 1 0 1 0 | 0 1 2 0 ..(..).. .o(x.).. ..(..).. ..(..)..&#x & | 0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * 36 * * * * * | 0 0 0 0 0 1 1 0 1 | 0 1 1 1 ..(..).. ..(..).. ..(..).. .x(o.)..&#x & | 0 2 1 | 0 0 0 0 1 2 0 0 | * * * * * * * * 36 * * * * | 0 0 1 0 0 0 1 0 1 | 0 1 1 1 .o(oo)o.3.o(oo)o. .o(oo)o.3.o(oo)o.&#xr | 0 2 2 | 0 0 0 0 0 2 2 0 | * * * * * * * * * 36 * * * | 0 0 0 0 0 0 0 1 2 | 0 0 2 1 cycle (BCED) ..(..).. ..(..).. .x(.o).. ..(..)..&#x & | 0 2 1 | 0 0 0 1 0 0 2 0 | * * * * * * * * * * 18 * * | 0 0 0 1 0 0 0 2 0 | 0 0 3 0 ..(..).. ..(..).. ..(..).. .x(.x)..&#x & | 0 2 2 | 0 0 0 0 1 0 2 1 | * * * * * * * * * * * 18 * | 0 0 0 1 0 0 0 0 2 | 0 0 2 1 ..(o.)..3..(x.).. ..(..).. ..(..).. & | 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * 6 | 0 0 0 1 0 2 0 0 0 | 0 1 2 0 ------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+-------- ox(..)..3oo(..).. ..(..).. ..(..)..&#x & ♦ 1 3 0 | 0 3 3 0 0 0 0 0 | 0 3 0 0 1 0 0 0 0 0 0 0 0 | 12 * * * * * * * * | 1 1 0 0 ox(..).. ..(..).. xx(..).. ..(..)..&#x & ♦ 2 4 0 | 1 4 2 2 0 0 0 0 | 0 2 2 0 0 1 0 0 0 0 0 0 0 | * 18 * * * * * * * | 1 0 1 0 ox(o.).. ..(..).. ..(..).. ox(o.)..&#xt & ♦ 1 4 1 | 0 4 2 0 2 4 0 0 | 0 2 0 2 0 0 2 0 2 0 0 0 0 | * * 18 * * * * * * | 0 1 1 0 ..(..).. ..(..).. xx(.o)..3ox(.x)..&#xt & ♦ 3 6 3 | 3 6 0 3 3 0 6 3 | 1 0 3 3 0 0 0 0 0 0 3 3 1 | * * * 6 * * * * * | 0 0 2 0 .x(..)..3.o(..).. .x(..).. ..(..).. & ♦ 0 6 0 | 0 0 6 3 0 0 0 0 | 0 0 0 0 2 3 0 0 0 0 0 0 0 | * * * * 6 * * * * | 1 0 1 0 .x(o.)..3.o(x.).. ..(..).. ..(..)..&#x & ♦ 0 3 3 | 0 0 3 0 0 6 0 3 | 0 0 0 0 1 0 3 3 0 0 0 0 1 | * * * * * 12 * * * | 0 1 1 0 ..(..).. .o(x.).. ..(..).. .x(o.)..&#xt & ♦ 0 2 2 | 0 0 0 0 1 4 0 1 | 0 0 0 0 0 0 0 2 2 0 0 0 0 | * * * * * * 18 * * | 0 1 0 1 .x(ou)x. ..(..).. .x(ou)x. ..(..)..&#xt ♦ 0 8 4 | 0 0 4 4 0 8 8 0 | 0 0 0 0 0 2 4 0 0 4 4 0 0 | * * * * * * * 9 * | 0 0 2 0 ..(..).. ..(..).. ..(..).. .x(ox)o.&#xr ♦ 0 3 3 | 0 0 0 0 1 4 3 1 | 0 0 0 0 0 0 0 1 1 2 0 1 0 | * * * * * * * * 36 | 0 0 1 1 cycle (BCED) ------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+-------- ox(..)..3oo(..).. xx(..).. ..(..)..&#x & ♦ 2 6 0 | 1 6 6 3 0 0 0 0 | 0 6 3 0 2 3 0 0 0 0 0 0 0 | 2 3 0 0 1 0 0 0 0 | 6 * * * ox(o.)..3oo(x.).. ..(..).. ox(o.)..&#xt & ♦ 1 6 3 | 0 6 6 0 3 12 0 3 | 0 6 0 3 2 0 6 6 6 0 0 0 1 | 2 0 3 0 0 2 3 0 0 | * 6 * * ox(ou)x. ..(..).. xx(uo)x.3ox(ox)o.&#xt & ♦ 3 18 9 | 3 12 12 9 6 24 18 6 | 1 6 6 6 2 6 12 6 6 12 9 6 2 | 0 3 3 2 1 2 0 3 6 | * * 6 * ..(..).. .o(xo)x. ..(..).. .x(ox)o.&#xr ♦ 0 4 4 | 0 0 0 0 2 8 4 2 | 0 0 0 0 0 0 0 4 4 4 0 2 0 | 0 0 0 0 0 0 2 0 4 | * * * 9
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