Acronym pero, J6
Name pentagonal rotunda,
half of icosidodecahedron
 
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Circumradius (1+sqrt(5))/2 = 1.618034
Vertex figure [(3,5)2], [3,5,10]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {5}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • between {3} and {10}:   arccos(sqrt[(5-2 sqrt(5))/15]) = 79.187683°
  • between {5} and {10}:   arccos(1/sqrt(5)) = 63.434949°
Confer
related Johnson solids:
gyepro   pocuro   pocuro   pobro   epgybro  
uniform relative:
id  
other symmetries
vov3ofx&#xt  
general polytopal classes:
Johnson solids   bistratic lace towers  
External
links
wikipedia   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

xox5ofx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/10] = 0.525731
                height(2,3) = sqrt[(5+sqrt(5))/10] = 0.850651
({5} || pseudo dual f-{5} || {10})

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

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