Acronym stacu
Name pentagrammic cupola,
star cupola
Circumradius sqrt(3)/2 = 0.866025
Vertex figures [3,4,5/2,4], [3,4,10/2]
Confer
more general:
n/d-cu  
non-Grünbaumian master:
stiscu  
general polytopal classes:
segmentohedra  

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


Incidence matrix according to Dynkin symbol

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

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

© 2004-2019
top of page