Acronym autic, J66
Name augmented truncated cube
VRML 
 ⭳ ©
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
  • between {3} and {4} (at join):   arccos(-sqrt[(3+2 sqrt(2))/6]) = 170.264390°
  • between {3} and {4} (at squacu lacings):   arccos[-sqrt(2/3)] = 144.735610°
  • between {3} and {8} (at join):   arccos[-sqrt(2/3)] = 144.735610°
  • between {3} and {8} (at tic edges):   arccos[-1/sqrt(3)] = 125.264390°
  • between {8} and {8}:   90°
Face vector 28, 48, 22
Confer
uniform relative:
tic  
related Johnson solids:
squacu   bautic  
general polytopal classes:
Johnson solids  
External
links 		wikipedia   polytopewiki   mathworld   quickfur

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}

© 2004-2025
top of page