Acronym gibil biro
Name great bilunabirotunda
 
 ©
Vertex figures [(3,5/2)2], [3,4,3/2,5/3], [3,(5/2)2]
Confer
uniform relative:
gike   gid  
related Johnson solids:
bilbiro  
general polytopal classes:
expanded kaleido-facetings  

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

As abstract polytope gibil biro is isomorphic to bilbiro, thereby replacing pentagrams by pentagons.


Incidence matrix according to Dynkin symbol

xVoVx xo(-v)ox&#xt    → outer heights = (1+sqrt(5))/4 = 0.809017
(V=vv=x-v)              inner heights = -1/2
({4} || pseudo V-line || pseudo ortho v-line || pseudo V-line || {4})

o.... o.( .)..     | 4 * * * * | 1 1 1 1 0 0 0 0 0 | 1 1 1 1 0 0 0
.o... .o( .)..     | * 2 * * * | 0 0 2 0 1 0 0 0 0 | 0 1 0 2 0 0 0
..o.. ..( o)..     | * * 2 * * | 0 0 0 2 0 2 0 0 0 | 0 0 1 2 1 0 0
...o. ..( .)o.     | * * * 2 * | 0 0 0 0 1 0 2 0 0 | 0 0 0 2 0 1 0
....o ..( .).o     | * * * * 4 | 0 0 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1
-------------------+-----------+-------------------+--------------
x.... ..( .)..     | 2 0 0 0 0 | 2 * * * * * * * * | 1 0 1 0 0 0 0
..... x.( .)..     | 2 0 0 0 0 | * 2 * * * * * * * | 1 1 0 0 0 0 0
oo... oo( .)..&#x  | 1 1 0 0 0 | * * 4 * * * * * * | 0 1 0 1 0 0 0
o.o.. o.( o)..&#x  | 1 0 1 0 0 | * * * 4 * * * * * | 0 0 1 1 0 0 0
.o.o. .o( .)o.&#x  | 0 1 0 1 0 | * * * * 2 * * * * | 0 0 0 2 0 0 0
..o.o ..( o).o&#x  | 0 0 1 0 1 | * * * * * 4 * * * | 0 0 0 1 1 0 0
...oo ..( .)oo&#x  | 0 0 0 1 1 | * * * * * * 4 * * | 0 0 0 1 0 1 0
....x ..( .)..     | 0 0 0 0 2 | * * * * * * * 2 * | 0 0 0 0 1 0 1
..... ..( .).x     | 0 0 0 0 2 | * * * * * * * * 2 | 0 0 0 0 0 1 1
-------------------+-----------+-------------------+--------------
x.... x.( .)..     | 4 0 0 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * * *
..... xo( .)..&#x  | 2 1 0 0 0 | 0 1 2 0 0 0 0 0 0 | * 2 * * * * *
x.o.. ..( .)..&#x  | 2 0 1 0 0 | 1 0 0 2 0 0 0 0 0 | * * 2 * * * *
ooooo oo( o)oo&#xt | 1 1 1 1 1 | 0 0 1 1 1 1 1 0 0 | * * * 4 * * *
..o.x ..( .)..&#x  | 0 0 1 0 2 | 0 0 0 0 0 2 0 1 0 | * * * * 2 * *
..... ..( .)ox&#x  | 0 0 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * 2 *
....x ..( .).x     | 0 0 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * 1
or
o.... o.( .)..     & | 8 * * | 1 1 1 1 0 | 1 1 1 1  [3,4,3/2,5/3]
.o... .o( .)..     & | * 4 * | 0 0 2 0 1 | 0 1 0 2  [3,(5/2)2]
..o.. ..( o)..       | * * 2 | 0 0 0 4 0 | 0 0 2 2  [(3,5/2)2]
---------------------+-------+-----------+--------
x.... ..( .)..     & | 2 0 0 | 4 * * * * | 1 0 1 0
..... x.( .)..     & | 2 0 0 | * 4 * * * | 1 1 0 0
oo... oo( .)..&#x  & | 1 1 0 | * * 8 * * | 0 1 0 1
o.o.. o.( o)..&#x  & | 1 0 1 | * * * 8 * | 0 0 1 1
.o.o. .o( .)o.&#x    | 0 2 0 | * * * * 2 | 0 0 0 2
---------------------+-------+-----------+--------
x.... x.( .)..     & | 4 0 0 | 2 2 0 0 0 | 2 * * *
..... xo( .)..&#x  & | 2 1 0 | 0 1 2 0 0 | * 4 * *
x.o.. ..( .)..&#x  & | 2 0 1 | 1 0 0 2 0 | * * 4 *
ooooo oo( o)oo&#xt   | 2 2 1 | 0 0 2 2 1 | * * * 4

oxVxo ov(-x)vo&#xt   → outer heights = (1+sqrt(5))/4 = 0.809017
(V=vv=x-v)              inner height = -1/2
(pt || pseudo (x,v)-{4} || pseudo (V,x)-{4} || pseudo (x,v)-{4} || pt)

o.... o.( .)..     | 1 * * * * | 4 0 0 0 0 0 0 0 | 2 2 0 0 0 0
.o... .o( .)..     | * 4 * * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 0 0
..o.. ..( o)..     | * * 4 * * | 0 0 1 0 1 1 0 0 | 0 1 0 1 1 0
...o. ..( .)o.     | * * * 4 * | 0 0 0 1 0 1 1 1 | 0 0 1 1 1 1
....o ..( .).o     | * * * * 1 | 0 0 0 0 0 0 0 4 | 0 0 0 0 2 2
-------------------+-----------+-----------------+------------
oo... oo( .)..&#x  | 1 1 0 0 0 | 4 * * * * * * * | 1 1 0 0 0 0
.x... ..( .)..     | 0 2 0 0 0 | * 2 * * * * * * | 1 0 1 0 0 0
.oo.. .o( o)..&#x  | 0 1 1 0 0 | * * 4 * * * * * | 0 1 0 1 0 0
.o.o. .o( .)o.&#x  | 0 1 0 1 0 | * * * 4 * * * * | 0 0 1 1 0 0
..... ..(-x)..     | 0 0 2 0 0 | * * * * 2 * * * | 0 1 0 0 1 0
..oo. ..( o)o.&#x  | 0 0 1 1 0 | * * * * * 4 * * | 0 0 0 1 1 0
...x. ..( .)..     | 0 0 0 2 0 | * * * * * * 2 * | 0 0 1 0 0 1
...oo ..( .)oo&#x  | 0 0 0 1 1 | * * * * * * * 4 | 0 0 0 0 1 1
-------------------+-----------+-----------------+------------
ox... ..( .)..&#x  | 1 2 0 0 0 | 2 1 0 0 0 0 0 0 | 2 * * * * *
..... ov(-x)..&#xt | 1 2 2 0 0 | 2 0 2 0 1 0 0 0 | * 2 * * * *
.x.x. ..( .)..&#x  | 0 2 0 2 0 | 0 1 0 2 0 0 1 0 | * * 2 * * *
.ooo. .o( o)o.&#xt | 0 1 1 1 0 | 0 0 1 1 0 1 0 0 | * * * 4 * *
..... ..(-x)vo&#xt | 0 0 2 2 1 | 0 0 0 0 1 2 0 2 | * * * * 2 *
...xo ..( .)..&#x  | 0 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * 2
or
o.... o.( .)..     & | 2 * * | 4 0 0 0 0 | 2 2 0 0  [(3,5/2)2]
.o... .o( .)..     & | * 8 * | 1 1 1 1 0 | 1 1 1 1  [3,4,3/2,5/3]
..o.. ..( o)..       | * * 4 | 0 0 2 0 1 | 0 2 0 1  [3,(5/2)2]
---------------------+-------+-----------+--------
oo... oo( .)..&#x  & | 1 1 0 | 8 * * * * | 1 1 0 0
.x... ..( .)..     & | 0 2 0 | * 4 * * * | 1 0 1 0
.oo.. .o( o)..&#x  & | 0 1 1 | * * 8 * * | 0 1 0 1
.o.o. .o( .)o.&#x    | 0 2 0 | * * * 4 * | 0 0 1 1
..... ..(-x)..       | 0 0 2 | * * * * 2 | 0 2 0 0
---------------------+-------+-----------+--------
ox... ..( .)..&#x  & | 1 2 0 | 2 1 0 0 0 | 4 * * *
..... ov(-x)..&#xt & | 1 2 2 | 2 0 2 0 1 | * 4 * *
.x.x. ..( .)..&#x    | 0 4 0 | 0 2 0 2 0 | * * 2 *
.ooo. .o( o)o.&#xt   | 0 2 1 | 0 0 2 1 0 | * * * 4

vxo ov(-x) oxV&#zxt   → both heights = 0
(V=vv=x-v)
(pseudo (v,o,o)-line || pseudo (x,v,x)-cube || pseudo (o,x,V)-{4})

o.. o.( .) o..     | 2 * * | 4 0 0 0 0 | 2 2 0 0  [(3,5/2)2]
.o. .o( .) .o.     | * 8 * | 1 1 1 1 0 | 1 1 1 1  [3,4,3/2,5/3]
..o ..( o) ..o     | * * 4 | 0 0 0 2 1 | 2 0 0 1  [3,(5/2)2]
-------------------+-------+-----------+--------
oo. oo( .) oo.&#x  | 1 1 0 | 8 * * * * | 1 1 0 0
.x. ..( .) ...     | 0 2 0 | * 4 * * * | 0 0 1 1
... ..( .) .x.     | 0 2 0 | * * 4 * * | 0 1 1 0
.oo .o( o) .oo&#x  | 0 1 1 | * * * 8 * | 1 0 0 1
... ..(-x) ...     | 0 0 2 | * * * * 2 | 2 0 0 0
-------------------+-------+-----------+--------
... ov(-x) ...&#xt | 1 2 2 | 2 0 0 2 1 | 4 * * *
... ..( .) ox.&#x  | 1 2 0 | 2 0 1 0 0 | * 4 * *
.x. ..( .) .x.     | 0 4 0 | 0 2 2 0 0 | * * 2 *
.xo ..( .) ...&#x  | 0 2 1 | 0 1 0 2 0 | * * * 4

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