Acronym | autic, J66 |
Name | augmented truncated cube |
© © | |
Vertex figures | [3,43], [3,4,3,8], [3,82] |
Lace city in approx. ASCII-art |
o q o x w w x w w w w x w w x |
x x x w w x o U o (U=qw=u+q=x+w) o U o x w w x | |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
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Face vector | 28, 48, 22 |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
xxoox4oxwwx&#xt → height(1,2) = height(2,3) = height(4,5) = 1/sqrt(2) = 0.707107 height(3,4) = 1 o....4o.... | 4 * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 augmented .o...4.o... | * 8 * * * | 0 1 1 1 1 0 0 0 0 | 0 1 1 1 1 0 0 join ..o..4..o.. | * * 4 * * | 0 0 0 0 2 1 0 0 0 | 0 0 0 1 2 0 0 upper ...o.4...o. | * * * 4 * | 0 0 0 0 0 1 2 0 0 | 0 0 0 0 2 1 0 lower ....o4....o | * * * * 8 | 0 0 0 0 0 0 1 1 1 | 0 0 0 0 1 1 1 bottom -----------------+-----------+-------------------+-------------- x.... ..... | 2 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0 0 oo...4oo...&#x | 1 1 0 0 0 | * 8 * * * * * * * | 0 1 1 0 0 0 0 .x... ..... | 0 2 0 0 0 | * * 4 * * * * * * | 0 1 0 1 0 0 0 ..... .x... | 0 2 0 0 0 | * * * 4 * * * * * | 0 0 1 0 1 0 0 .oo..4.oo..&#x | 0 1 1 0 0 | * * * * 8 * * * * | 0 0 0 1 1 0 0 ..oo.4..oo.&#x | 0 0 1 1 0 | * * * * * 4 * * * | 0 0 0 0 2 0 0 ...oo4...oo&#x | 0 0 0 1 1 | * * * * * * 8 * * | 0 0 0 0 1 1 0 ..... ....x | 0 0 0 0 2 | * * * * * * * 4 * | 0 0 0 0 1 0 1 ....x ..... | 0 0 0 0 2 | * * * * * * * * 4 | 0 0 0 0 0 1 1 -----------------+-----------+-------------------+-------------- x....4o.... | 4 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 1 * * * * * * top {4} xx... .....&#x | 2 2 0 0 0 | 1 2 1 0 0 0 0 0 0 | * 4 * * * * * augmenting {4} ..... ox...&#x | 1 2 0 0 0 | 0 2 0 1 0 0 0 0 0 | * * 4 * * * * augmenting {3} .xo.. .....&#x | 0 2 1 0 0 | 0 0 1 0 2 0 0 0 0 | * * * 4 * * * upper {3} ..... .xwwx&#xt | 0 2 2 2 2 | 0 0 0 1 2 2 2 1 0 | * * * * 4 * * latteral {8} ...ox .....&#x | 0 0 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * 4 * lower {3} ....x4....x | 0 0 0 0 8 | 0 0 0 0 0 0 0 4 4 | * * * * * * 1 bottom {8}
(oq)(xw)ww(xw) (qo)(wx)ww(wx)&#xt → height(1,2) = height(2,3) = height(4,5) = 1/sqrt(2) = 0.707107 height(3,4) = 1 (o.)(..)..(..) (o.)(..)..(..)&#x & | 4 * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 augmented (..)(o.)..(..) (..)(o.)..(..)&#x & | * 8 * * * | 0 1 1 1 1 0 0 0 0 | 0 1 1 1 1 0 0 join (..)(..)o.(..) (..)(..)o.(..)&#x | * * 4 * * | 0 0 0 0 2 1 0 0 0 | 0 0 0 1 2 0 0 upper (..)(..).o(..) (..)(..).o(..)&#x | * * * 4 * | 0 0 0 0 0 1 2 0 0 | 0 0 0 0 2 1 0 lower (..)(..)..(o.) (..)(..)..(o.)&#x & | * * * * 8 | 0 0 0 0 0 0 1 1 1 | 0 0 0 0 1 1 1 bottom ------------------------------------+-----------+-------------------+-------------- (oo)(..)..(..) (oo)(..)..(..)&#x | 2 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0 0 (o.)(o.)..(..) (o.)(o.)..(..)&#x & | 1 1 0 0 0 | * 8 * * * * * * * | 0 1 1 0 0 0 0 (..)(oo)..(..) (..)(oo)..(..)&#x | 0 2 0 0 0 | * * 4 * * * * * * | 0 1 0 1 0 0 0 (..)(x.)..(..) (..)(..)..(..) & | 0 2 0 0 0 | * * * 4 * * * * * | 0 0 1 0 1 0 0 (..)(o.)o.(..) (..)(o.)o.(..)&#x & | 0 1 1 0 0 | * * * * 8 * * * * | 0 0 0 1 1 0 0 (..)(..)oo(..) (..)(..)oo(..)&#x | 0 0 1 1 0 | * * * * * 4 * * * | 0 0 0 0 2 0 0 (..)(..).o(o.) (..)(..).o(o.)&#x & | 0 0 0 1 1 | * * * * * * 8 * * | 0 0 0 0 1 1 0 (..)(..)..(x.) (..)(..)..(..)&#x & | 0 0 0 0 2 | * * * * * * * 4 * | 0 0 0 0 1 0 1 (..)(..)..(oo) (..)(..)..(oo)&#x | 0 0 0 0 2 | * * * * * * * * 4 | 0 0 0 0 0 1 1 ------------------------------------+-----------+-------------------+-------------- (oq)(..)..(..) (qo)(..)..(..)&#zx | 4 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 1 * * * * * * top {4} (oo)(oo)..(..) (oo)(oo)..(..)&#xr | 2 2 0 0 0 | 1 2 1 0 0 0 0 0 0 | * 4 * * * * * augmenting {4} (o.)(x.)..(..) (..)(..)..(..)&#x & | 1 2 0 0 0 | 0 2 0 1 0 0 0 0 0 | * * 4 * * * * augmenting {3} (..)(oo)o.(..) (..)(oo)o.(..)&#x | 0 2 1 0 0 | 0 0 1 0 2 0 0 0 0 | * * * 4 * * * upper {3} (..)(x.)ww(x.) (..)(..)..(..)&#xt & | 0 2 2 2 2 | 0 0 0 1 2 2 2 1 0 | * * * * 4 * * latteral {8} (..)(..).o(oo) (..)(..).o(oo)&#x | 0 0 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * 4 * lower {3} (..)(..)..(xw) (..)(..)..(wx)&#zx | 0 0 0 0 8 | 0 0 0 0 0 0 0 4 4 | * * * * * * 1 bottom {8}
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