Acronym autipip
Name augmented-triangular-prism prism
Circumradius ...
Coordinates
  1. (1/2, 0, 0, 1/sqrt(2))            & all changes of sign in 1st coord.
    (top line)
  2. (1/2, 1/2, 1/2, 0)                 & all changes of sign
    (joining cube)
  3. (1/2, 1/2, 0, -sqrt(3)/2)       & all changes of sign in 1st & 2nd coord.
    (bottom square)
Dihedral angles
  • 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 autip and cube:   90°
  • at {4} between cube and trip (within tisdip-part):   90°
  • at {3} between autip and trip:   90°
  • at {4} between cube and cube:   60°
Face vector 14, 33, 29, 10
Confer
uniform relative:
tisdip  
blend-component:
tisdip   squippyp  
related segmentochora:
squippyp  
related CRFs:
bauautipip   aubautipip   tautipip   gyautisdip  
general polytopal classes:
bistratic lace towers  

Incidence matrix according to Dynkin symbol

xxx xxo oxo&#xt   → height(1,2) = 1/sqrt(2) = 0.707107
                    height(2,3) = sqrt(3)/2 = 0.866025
({4} || (pseudo) cube || line)

o.. o.. o..     | 4 * * | 1 1 2 0 0 0 0 0 | 1 2 2 1 0 0 0 0 0 | 2 1 1 0 0
.o. .o. .o.     | * 8 * | 0 0 1 1 1 1 1 0 | 0 1 1 1 1 1 1 1 1 | 1 1 1 1 1
..o ..o ..o     | * * 2 | 0 0 0 0 0 0 4 1 | 0 0 0 0 0 0 4 2 2 | 0 0 1 2 2
----------------+-------+-----------------+-------------------+----------
x.. ... ...     | 2 0 0 | 2 * * * * * * * | 1 2 0 0 0 0 0 0 0 | 2 1 0 0 0
... x.. ...     | 2 0 0 | * 2 * * * * * * | 1 0 2 0 0 0 0 0 0 | 2 0 1 0 0
oo. oo. oo.&#x  | 1 1 0 | * * 8 * * * * * | 0 1 1 1 0 0 0 0 0 | 1 1 1 0 0
.x. ... ...     | 0 2 0 | * * * 4 * * * * | 0 1 0 0 1 1 1 0 0 | 1 1 0 1 1
... .x. ...     | 0 2 0 | * * * * 4 * * * | 0 0 1 0 1 0 0 1 0 | 1 0 1 1 0
... ... .x.     | 0 2 0 | * * * * * 4 * * | 0 0 0 1 0 1 0 0 1 | 0 1 1 0 1
.oo .oo .oo&#x  | 0 1 1 | * * * * * * 8 * | 0 0 0 0 0 0 1 1 1 | 0 0 1 1 1
..x ... ...     | 0 0 2 | * * * * * * * 1 | 0 0 0 0 0 0 4 0 0 | 0 0 0 2 2
----------------+-------+-----------------+-------------------+----------
x.. x.. ...     | 4 0 0 | 2 2 0 0 0 0 0 0 | 1 * * * * * * * * | 2 0 0 0 0
xx. ... ...&#x  | 2 2 0 | 1 0 2 1 0 0 0 0 | * 4 * * * * * * * | 1 1 0 0 0
... xx. ...&#x  | 2 2 0 | 0 1 2 0 1 0 0 0 | * * 4 * * * * * * | 1 0 1 0 0
... ... ox.&#x  | 1 2 0 | 0 0 2 0 0 1 0 0 | * * * 4 * * * * * | 0 1 1 0 0
.x. .x. ...     | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * 2 * * * * | 1 0 0 1 0
.x. ... .x.     | 0 4 0 | 0 0 0 2 0 2 0 0 | * * * * * 2 * * * | 0 1 0 0 1
.xx ... ...&#x  | 0 2 2 | 0 0 0 1 0 0 2 1 | * * * * * * 4 * * | 0 0 0 1 1
... .xo ...&#x  | 0 2 1 | 0 0 0 0 1 0 2 0 | * * * * * * * 4 * | 0 0 1 1 0
... ... .xo&#x  | 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * 4 | 0 0 1 0 1
----------------+-------+-----------------+-------------------+----------
xx. xx. ...&#x  ♦ 4 4 0 | 2 2 4 2 2 0 0 0 | 1 2 2 0 1 0 0 0 0 | 2 * * * *
xx. ... ox.&#x  ♦ 2 4 0 | 1 0 4 2 0 2 0 0 | 0 2 0 2 0 1 0 0 0 | * 2 * * *
... xxo oxo&#xt ♦ 2 4 1 | 0 1 4 0 2 2 4 0 | 0 0 2 2 0 0 0 2 2 | * * 2 * *
.xx .xo ...&#x  ♦ 0 4 2 | 0 0 0 2 2 0 4 1 | 0 0 0 0 1 0 2 2 0 | * * * 2 *
.xx ... .xo&#x  ♦ 0 4 2 | 0 0 0 2 0 2 4 1 | 0 0 0 0 0 1 2 0 2 | * * * * 2

© 2004-2024
top of page