Acronym bautipip
Name biaugmented-triangular-prism prism
Coordinates
  1. (1/2, 1/2, 0, 1/sqrt(3))                & all changes of sign in first 3 coords.
    (biaugmentation rim)
  2. (1/2, 0, A/2, A/sqrt(12))             & all changes of sign in first 3 coords.
    (augmentation wedges)
  3. (1/2, 1/2, 1/2, -1/sqrt(12))          & all changes of sign in first 3 coords.
    (opposite cube)
where A = (1+sqrt(6))/2 = 1.724745
Dihedral angles
  • at {4} between trip and trip (across biaugmentation rim):   arccos[-(1+2 sqrt(6))/6] = 169.471221°
  • at {4} between trip and trip (across augmentation rim):   arccos[-sqrt(2/3)] = 144.735610°
  • at {4} between cube and trip (across augmentation rim):   arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610°
  • at {4} between trip and trip (within squippyp-part):   arccos(-1/3) = 109.471221°
  • at {4} between bautip and cube:   90°
  • at {3} between bautip and trip:   90°
  • at {4} between cube and trip (within tisdip-part):   90°
Confer
uniform relative:
tisdip  
blend-component:
squippyp   tisdip  
related segmentochora:
squippyp  
related CRFs:
autipip   aubautipip   tautipip  
general polytopal classes:
bistratic lace towers  

Incidence matrix according to Dynkin symbol

xxx xox oAx&#xt   → height(1,2) = (3-sqrt(6))/sqrt(48) = 0.079459
                    height(2,3) = (3+sqrt(6))/sqrt(48) = 0.786566
                    where A = (1+sqrt(6))/2 = 1.724745
(square || (pseudo) (x,A)-rectangle || cube)

o.. o.. o..     | 4 * * | 1 1 2 2 0 0 0 0 0 | 1 2 2 2 2 1 0 0 0 0 0 | 2 2 1 1 0 0
.o. .o. .o.     | * 4 * | 0 0 2 0 1 2 0 0 0 | 0 2 1 2 0 0 2 1 0 0 0 | 1 2 1 0 1 0
..o ..o ..o     | * * 8 | 0 0 0 1 0 1 1 1 1 | 0 0 0 1 1 1 1 1 1 1 1 | 0 1 1 1 1 1
----------------+-------+-------------------+-----------------------+------------
x.. ... ...     | 2 0 0 | 2 * * * * * * * * | 1 2 0 0 2 0 0 0 0 0 0 | 2 2 0 1 0 0
... x.. ...     | 2 0 0 | * 2 * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 | 2 0 1 0 0 0
oo. oo. oo.&#x  | 1 1 0 | * * 8 * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0
o.o o.o o.o&#x  | 1 0 1 | * * * 8 * * * * * | 0 0 0 1 1 1 0 0 0 0 0 | 0 1 1 1 0 0
.x. ... ...     | 0 2 0 | * * * * 2 * * * * | 0 2 0 0 0 0 2 0 0 0 0 | 1 1 0 0 1 0
.oo .oo .oo&#x  | 0 1 1 | * * * * * 8 * * * | 0 0 0 1 0 0 1 1 0 0 0 | 0 1 1 0 1 0
..x ... ...     | 0 0 2 | * * * * * * 4 * * | 0 0 0 0 1 0 1 0 1 1 0 | 0 1 0 1 1 1
... ..x ...     | 0 0 2 | * * * * * * * 4 * | 0 0 0 0 0 0 0 1 1 0 1 | 0 0 1 0 1 1
... ... ..x     | 0 0 2 | * * * * * * * * 4 | 0 0 0 0 0 1 0 0 0 1 1 | 0 0 1 1 0 1
----------------+-------+-------------------+-----------------------+------------
x.. x.. ...     | 4 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 2 0 0 0 0 0
xx. ... ...&#x  | 2 2 0 | 1 0 2 0 1 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0 0
... xo. ...&#x  | 2 1 0 | 0 1 2 0 0 0 0 0 0 | * * 4 * * * * * * * * | 1 0 1 0 0 0
ooo ooo ooo&#x  | 1 1 1 | 0 0 1 1 0 1 0 0 0 | * * * 8 * * * * * * * | 0 1 1 0 0 0
x.x ... ...&#x  | 2 0 2 | 1 0 0 2 0 0 1 0 0 | * * * * 4 * * * * * * | 0 1 0 1 0 0
... ... o.x&#x  | 1 0 2 | 0 0 0 2 0 0 0 0 1 | * * * * * 4 * * * * * | 0 0 1 1 0 0
.xx ... ...&#x  | 0 2 2 | 0 0 0 0 1 2 1 0 0 | * * * * * * 4 * * * * | 0 1 0 0 1 0
... .ox ...&#x  | 0 1 2 | 0 0 0 0 0 2 0 1 0 | * * * * * * * 4 * * * | 0 0 1 0 1 0
..x ..x ...     | 0 0 4 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * 2 * * | 0 0 0 0 1 1
..x ... ..x     | 0 0 4 | 0 0 0 0 0 0 2 0 2 | * * * * * * * * * 2 * | 0 0 0 1 0 1
... ..x ..x     | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * 2 | 0 0 1 0 0 1
----------------+-------+-------------------+-----------------------+------------
xx. xo. ...&#x   4 2 0 | 2 2 4 0 1 0 0 0 0 | 1 2 2 0 0 0 0 0 0 0 0 | 2 * * * * *
xxx ... ...&#x   2 2 2 | 1 0 2 2 1 2 1 0 0 | 0 1 0 2 1 0 1 0 0 0 0 | * 4 * * * *
... xox oAx&#xt  2 2 4 | 0 1 4 4 0 4 0 2 2 | 0 0 2 4 0 2 0 2 0 0 1 | * * 2 * * *
x.x ... o.x&#x   2 0 4 | 1 0 0 4 0 0 2 0 2 | 0 0 0 0 2 2 0 0 0 1 0 | * * * 2 * *
.xx .ox ...&#x   0 2 4 | 0 0 0 0 1 4 2 2 0 | 0 0 0 0 0 0 2 2 1 0 0 | * * * * 2 *
..x ..x ..x      0 0 8 | 0 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 2 2 2 | * * * * * 1

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