The Elongated Pentagonal Rotunda
The elongated pentagonal rotunda is the 21st Johnson solid (J21). It has 30 vertices and 27 faces (10 equilateral triangles, 10 squares, 6 pentagons, and 1 decagon).
The elongated pentagonal rotunda can be constructed by attaching a decagonal prism to a pentagonal rotunda (J6), lengthening it; hence the name elongated.
Projections
Here are some views of the elongated pentagonal rotunda from various angles:
Projection  Envelope  Description 

Regular decagon  Top view. 

Octagon  Front view. 

Heptagon  Side view. 
Coordinates
The Cartesian coordinates of the elongated pentagonal rotunda with edge length 2 are:
 (0, √((10+2√5)/5), 1+√((20+8√5)/5))
 (±1, √((5+2√5)/5), 1+√((20+8√5)/5))
 (±φ, √((5√5)/10), 1+√((20+8√5)/5))
 (0, √((20+8√5)/5), 1+√((10+2√5)/5))
 (±φ, √((25+11√5)/10), 1+√((10+2√5)/5))
 (±φ^2, √((5+√5)/10), 1+√((10+2√5)/5))
 (±1, ±√(3+4φ), ±1)
 (±φ^2, ±√(2+φ), ±1)
 (±2φ, 0, ±1)
where φ=(1+√5)/2 is the Golden Ratio.