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Similar to thawro, likewise githawro can be obtained by means of an expanded kaleido-faceting, but here by starting with gike instead.

This polyhedron further is related not only to gid (that central 3 pentagrams plus 4 triangles patch) but also to qrid (the 3 lunes out of a square and 2 attached triangles each).

As abstract polytope githawro is isomorphic to thawro, thereby replacing pentagrams by pentagons.

Incidence matrix according to Dynkin symbol

x(-v)ox3oxVx&#xt   → height(1,2) = height(3,4) = 1/sqrt(3) = 0.577350
(V=vv=x-v)        height(2,3) = -sqrt[(3+sqrt(5))/6] = -0.934172
({3} || pseudo (v,x)-{6} || pseudo dual V-{3} || {6})

o( .)..3o...     | 3 * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 0 0  [(3,5/2)2]
.( o)..3.o..     | * 6 * * | 0 1 1 1 1 0 0 0 | 0 1 1 1 1 0 0  [3,4,3/2,5/3]
.( .)o.3..o.     | * * 3 * | 0 0 0 2 0 2 0 0 | 0 1 0 0 2 1 0  [33,5/3]
.( .).o3...o     | * * * 6 | 0 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1  [3,3/2,4/3,6]
-----------------+---------+-----------------+--------------
x( .).. ....     | 2 0 0 0 | 3 * * * * * * * | 1 1 0 0 0 0 0
o( o)..3oo..&#x  | 1 1 0 0 | * 6 * * * * * * | 0 1 1 0 0 0 0
.( .).. .x..     | 0 2 0 0 | * * 3 * * * * * | 0 0 1 1 0 0 0
.( o)o.3.oo.&#x  | 0 1 1 0 | * * * 6 * * * * | 0 1 0 0 1 0 0
.( o).o3.o.o&#x  | 0 1 0 1 | * * * * 6 * * * | 0 0 0 1 1 0 0
.( .)oo3..oo&#x  | 0 0 1 1 | * * * * * 6 * * | 0 0 0 0 1 1 0
.( .).x ....     | 0 0 0 2 | * * * * * * 3 * | 0 0 0 0 0 1 1
.( .).. ...x     | 0 0 0 2 | * * * * * * * 3 | 0 0 0 1 0 0 1
-----------------+---------+-----------------+--------------
x( .)..3o...     | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 1 * * * * * *
x(-v)o. ....&#xt | 2 2 1 0 | 1 2 0 2 0 0 0 0 | * 3 * * * * *  {5/2}
.( .).. ox..&#x  | 1 2 0 0 | 0 2 1 0 0 0 0 0 | * * 3 * * * *
.( .).. .x.x&#x  | 0 2 0 2 | 0 0 1 0 2 0 0 1 | * * * 3 * * *  {4}
.( o)oo3.ooo&#xt | 0 1 1 1 | 0 0 0 1 1 1 0 0 | * * * * 6 * *
.( .)ox ....&#x  | 0 0 1 2 | 0 0 0 0 0 2 1 0 | * * * * * 3 *
.( .).x3...x     | 0 0 0 6 | 0 0 0 0 0 0 3 3 | * * * * * * 1  {6}