The Elongated Pentagonal Cupola
The elongated pentagonal cupola is the 20th Johnson solid (J20). It has 25 vertices and 22 faces (5 equilateral triangles, 15 squares, 1 pentagon, and 1 decagon).
The elongated pentagonal cupola can be constructed by attaching a decagonal prism to a pentagonal cupola (J5), lengthening it; hence the name elongated.
Projections
Here are some views of the elongated pentagonal cupola from various angles:
Projection  Envelope  Description 

Regular decagon  Top view. 

Hexagon  Front view. 

Hexagon  Side view. 
Coordinates
The Cartesian coordinates of the elongated pentagonal cupola with edge length 2 are:
 (0, √((10+2√(5))/5), 1+2√((3φ)/5))
 (±φ, √((5√(5))/10), 1+2√((3φ)/5))
 (±1, √((5+2√(5))/5), 1+2√((3φ)/5))
 (±2φ, 0, ±1)
 (±1, ±√(3+4φ), ±1)
 (±φ^{2}, ±√(2+φ), ±1)
where φ=(1+√5)/2 is the Golden Ratio.