Acronym	rapescu
Name	retrograde pentagonal cuploid, retrograde pentagonal semicupola
	© embedding of rapescu within sidtid
Circumradius	sqrt(3)/2 = 0.866025
Vertex figures	[3,4,5/4,4], [3,4,3/2,4/3]/0
Face vector	10, 20, 11
Confer	more general: n/d-cu   uniform relative: sidtid   general polytopal classes: segmentohedra
External links

Rapescu is an edge-faceting of sidtid, in fact it uses triangles of it and squares of rhom, the inscribed compound of 5 cube, as well as the pentagon of the inscribed ditdid or gidtid.

As a cuploid it has a pseudo bottom face. That one is the withdrawn {10/4} of the corresponding cupola.

As abstract polytope rapescu is isomorphic to stiscu, thereby replacing the retrograde pentagon by a (prograde) pentagram, while pseudo pentagram would become a pseudo pentagon.

Incidence matrix according to Dynkin symbol

reduced(xx5/4ox&#x by x5/4x)   → height = sqrt((5-sqrt(5))/10) = 0.525731
({5/4} || pseudo {10/4})

o.5/4o.             | 5 * | 2  2 0 | 1 2 1
.o5/4.o             | * 5 | 0  2 2 | 0 2 2
--------------------+-----+--------+------
x.   ..             | 2 0 | 5  * * | 1 1 0
oo5/4oo&#x          | 1 1 | * 10 * | 0 1 1
.x   ..  &  ..   .x | 0 2 | *  * 5 | 0 1 1  (those edges get identified)
--------------------+-----+--------+------
x.5/4o.             | 5 0 | 5  0 0 | 1 * *
xx   ..&#x          | 2 2 | 1  2 1 | * 5 *
..   ox&#x          | 1 2 | 0  2 1 | * * 5