Acronym tautip, J51
Name triaugmented trigonal prism
 
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Vertex figure [34], [35]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
(at margins)
  • at lacing edges of central prism:   arccos[-(1+2 sqrt(6))/6] = 169.471221°
  • at base edges of central prism:   arccos[-sqrt(2/3)] = 144.735610°
  • at lacing edges of augmenting pyramids:   arccos(-1/3) = 109.471221°
Confer
blend-component:
trip   squippy  
related Johnson solids:
autip   bautip  
general polytopal classes:
Johnson solids   deltahedra   bistratic lace towers  
External
links
wikipedia   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

xox3oAo&#xt   → both heights = 1/2
                where A = (1+sqrt(6))/2 = 1.724745
({3} || (pseudo) dual A-{3} || {3})

o..3o..    & | 6 * | 2  2 1 | 1 2 2
.o.3.o.      | * 3 | 0  4 0 | 0 2 2
-------------+-----+--------+------
x.. ...    & | 2 0 | 6  * * | 1 1 0
oo.3oo.&#x & | 1 1 | * 12 * | 0 1 1
o.o3o.o&#x   | 2 0 | *  * 3 | 0 0 2
-------------+-----+--------+------
x..3o..    & | 3 0 | 3  0 0 | 2 * *
xo. ...&#x & | 2 1 | 1  2 0 | * 6 *
ooo3ooo&#x   | 2 1 | 0  2 1 | * * 6

xo3oA xo&#zx   → height = 0
                 where A = (1+sqrt(6))/2 = 1.724745
(tegum sum of trip and dual A-{3})

o.3o. o.    | 6 * | 2 1  2 | 1 2 2
.o3.o .o    | * 3 | 0 0  4 | 0 2 2
------------+-----+--------+------
x. .. ..    | 2 0 | 6 *  * | 1 1 0
.. .. x.    | 2 0 | * 3  * | 0 0 2
oo3oo oo&#x | 1 1 | * * 12 | 0 1 1
------------+-----+--------+------
x.3o. ..    | 3 0 | 3 0  0 | 2 * *
xo .. ..&#x | 2 1 | 1 0  2 | * 6 *
.. .. xo&#x | 2 1 | 0 1  2 | * * 6

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