Acronym pocuro, J32
Name pentagonal orthocupolarotunda
 
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Vertex figure [(3,5)2], [3,4,3,5], [3,4,5,4]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4} (cupolaic):   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {4} and {5} (cupolaic):   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
  • between {3} and {5} (rotundal):   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • 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:
pero   pecu   pegycuro   epocuro   gyepcuro   bilbiro   thawro  
general polytopal classes:
Johnson solids   expanded kaleido-facetings  
External
links
wikipedia   mathworld   quickfur  

The right pic shows how pocuro can be obtained by means of a expanded kaleido-faceting from ike. And this relation too is why pocuro occures sometimes as a cell within CRFs.


Incidence matrix according to Dynkin symbol

xoxx5ofxo&#xt   → outer heights = sqrt[(5-sqrt(5))/10] = 0.525731
                  inner height = sqrt[(5+sqrt(5))/10] = 0.850651
({5} || pseudo dual f-{5} || pseudo {10} || para {5})

o...5o...     | 5 *  * * | 2  2  0 0 0  0 0 | 1 2 1 0 0 0 0
.o..5.o..     | * 5  * * | 0  2  2 0 0  0 0 | 0 1 2 1 0 0 0
..o.5..o.     | * * 10 * | 0  0  1 1 1  1 0 | 0 0 1 1 1 1 0
...o5...o     | * *  * 5 | 0  0  0 0 0  2 2 | 0 0 0 0 2 1 1
--------------+----------+------------------+--------------
x... ....     | 2 0  0 0 | 5  *  * * *  * * | 1 1 0 0 0 0 0
oo..5oo..&#x  | 1 1  0 0 | * 10  * * *  * * | 0 1 1 0 0 0 0
.oo.5.oo.&#x  | 0 1  1 0 | *  * 10 * *  * * | 0 0 1 1 0 0 0
..x. ....     | 0 0  2 0 | *  *  * 5 *  * * | 0 0 0 1 1 0 0
.... ..x.     | 0 0  2 0 | *  *  * * 5  * * | 0 0 1 0 0 1 0
..oo5..oo&#x  | 0 0  1 1 | *  *  * * * 10 * | 0 0 0 0 1 1 0
...x ....     | 0 0  0 2 | *  *  * * *  * 5 | 0 0 0 0 1 0 1
--------------+----------+------------------+--------------
x...5o...     | 5 0  0 0 | 5  0  0 0 0  0 0 | 1 * * * * * *
xo.. ....&#x  | 2 1  0 0 | 1  2  0 0 0  0 0 | * 5 * * * * *
.... ofx.&#xt | 1 2  2 0 | 0  2  2 0 1  0 0 | * * 5 * * * *
.ox. ....&#x  | 0 1  2 0 | 0  0  2 1 0  0 0 | * * * 5 * * *
..xx ....&#x  | 0 0  2 2 | 0  0  0 1 0  2 1 | * * * * 5 * *
.... ..xo&#x  | 0 0  2 1 | 0  0  0 0 1  2 0 | * * * * * 5 *
...x5...o     | 0 0  0 5 | 0  0  0 0 0  0 5 | * * * * * * 1

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