Acronym rastacu
Name retrograde pentagrammic cupola,
5/3-cupola
 
Circumradius sqrt[-sqrt(5)+11/4] = 0.716891
Vertex figures [3,4,5/3,4], [3,4,10/3]
Dihedral angles
  • between {3} and {10/3}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
  • between {3} and {4}:   arccos((sqrt(5)-1)/sqrt(12)) = 69.094843°
  • between {4} and {5/2}:   arccos(sqrt[(5-sqrt(5))/10]) = 58.282526°
  • between {4} and {10/3}:   arccos(sqrt[(5-sqrt(5))/10]) = 58.282526°
Confer
general cupolae:
n/d-cu  
uniform relative:
qrid  
related Johnson solids:
pecu  
general polytopal classes:
segmentohedra  

As abstract polytope rastacu is isomorphic to pecu, thereby replacing the retrograde pentagram by a (prograde) pentagon and the decagram by a decagon. Or it is isomorphic to stacu, thereby replacing the retrograde pentagram by a prograde pentagram and the decagram by a Grünbaumian {10/2}.


Incidence matrix according to Dynkin symbol

xx5/3ox&#x   → height = sqrt((5+sqrt(5))/10) = 0.850651
({5/2} || {10/3})

o.5/3o.    | 5  * | 2  2 0 0 | 1 2 1 0
.o5/3.o    | * 10 | 0  1 1 1 | 0 1 1 1
-----------+------+----------+--------
x.   ..    | 2  0 | 5  * * * | 1 1 0 0
oo5/3oo&#x | 1  1 | * 10 * * | 0 1 1 0
.x   ..    | 0  2 | *  * 5 * | 0 1 0 1
..   .x    | 0  2 | *  * * 5 | 0 0 1 1
-----------+------+----------+--------
x.5/3o.    | 5  0 | 5  0 0 0 | 1 * * *
xx   ..&#x | 2  2 | 1  2 1 0 | * 5 * *
..   ox&#x | 1  2 | 0  2 0 1 | * * 5 *
.x5/3.x    | 0 10 | 0  0 5 5 | * * * 1

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