Acronym thawro, J92
Name triangular hebesphenorotunda
 
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Vertex figure [(3,5)2], [3,4,3,5], [33,5], [32,4,6]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4} (lunaic):   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {3} and {5} (rotundal):   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685°
  • between {3} and {6}:   arccos(-sqrt(5)/3) = 138.189685°
  • between {4} and {6}:   arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157°
  • between {3} and {4} (across rim):   arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157°
  • between {3} and {5} (across rim):   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
Confer
uniform relative:
ike   id   srid  
related Johnson solids:
pocuro   bilbiro  
general polytopal classes:
Johnson solids   expanded kaleido-facetings  
External
links
wikipedia   mathworld   quickfur

At the first view this polyhedron looks odd, a real find. But consider the base hexagon being scaled by τ = (1+sqrt(5))/2, keeping its orientation and remaining coplanar. The lacing edges incident to that hexagon thereby all keep their lengths. Thus that figure would then be described by xfof3oxFf&#xt. The f-hexagon incident faces then are golden x-x-f triangles, respectively x-x-x-f trapeziae. Both are complementary parts of regular pentagons. And in fact, this derived figure is nothing but a triangle face parallel rotunda (i.e. half) of the id.

The right pic shows however how thawro can be obtained directly by means of an expanded kaleido-faceting from ike. And this relation too is why thawro occures not too seldomly as a cell within CRFs.

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


Incidence matrix according to Dynkin symbol

xfox3oxFx&#xt   → height(1,2) = height(3,4) = 1/sqrt(3) = 0.577350
(F=ff=x+f)        height(2,3) = sqrt[(3-sqrt(5))/6] = 0.356822
({3} || pseudo (f,x)-{6} || pseudo dual F-{3} || {6})

o...3o...     | 3 * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 0 0  [(3,5)2]
.o..3.o..     | * 6 * * | 0 1 1 1 1 0 0 0 | 0 1 1 1 1 0 0  [3,4,3,5]
..o.3..o.     | * * 3 * | 0 0 0 2 0 2 0 0 | 0 1 0 0 2 1 0  [33,5]
...o3...o     | * * * 6 | 0 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1  [32,4,6]
--------------+---------+-----------------+--------------
x... ....     | 2 0 0 0 | 3 * * * * * * * | 1 1 0 0 0 0 0
oo..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
.oo.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 * * * * * *
xfo. ....&#xt | 2 2 1 0 | 1 2 0 2 0 0 0 0 | * 3 * * * * *  {5}
.... 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}
.ooo3.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}

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