Acronym autip, J49
Name augmented triangular prism
 
 © ©
Vertex figures [34], [33,4], [3,42]
Coordinates
  1. (0, 0, 1/sqrt(2))
    (augmentation vertex)
  2. (1/2, 1/2, 0)                 & all changes of sign
    (joining square)
  3. (1/2, 0, -sqrt(3)/2)       & all changes of sign in 1st coord.
    (opposite line)
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {3} (across augmentation rim):   arccos[-sqrt(2/3)] = 144.735610°
  • between {3} and {4} (across augmentation rim):   arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610°
  • between {3} and {3} (within squippy-part):   arccos(-1/3) = 109.471221°
  • between {3} and {4} (within trip-part):   90°
  • between {4} and {4}:   60°
Confer
uniform relative:
trip  
related Johnson solids:
squippy   bautip   tautip   etripy  
general polytopal classes:
Johnson solids   bistratic lace towers  
External
links
wikipedia   mathworld   quickfur  

While in autip the lacing square of trip gets augmented with a pyramid (squippy), etripy similarily would have the trigonal base being augmented with a pyramid (tet).


Incidence matrix according to Dynkin symbol

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

o.. o..    | 1 * * | 4 0 0 0 0 | 2 2 0 0
.o. .o.    | * 4 * | 1 1 1 1 0 | 1 1 1 1
..o ..o    | * * 2 | 0 0 0 2 1 | 0 0 2 1
-----------+-------+-----------+--------
oo. oo.&#x | 1 1 0 | 4 * * * * | 1 1 0 0
.x. ...    | 0 2 0 | * 2 * * * | 1 0 1 0
... .x.    | 0 2 0 | * * 2 * * | 0 1 0 1
.oo .oo&#x | 0 1 1 | * * * 4 * | 0 0 1 1
..x ...    | 0 0 2 | * * * * 1 | 0 0 2 0
-----------+-------+-----------+--------
ox. ...&#x | 1 2 0 | 2 1 0 0 0 | 2 * * *
... ox.&#x | 1 2 0 | 2 0 1 0 0 | * 2 * *
.xx ...&#x | 0 2 2 | 0 1 0 2 1 | * * 2 *
... .xo&#x | 0 2 1 | 0 0 1 2 0 | * * * 2

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