The Gyroelongated Pentagonal Pyramid
The gyroelongated pentagonal pyramid is the 11th Johnson solid (J11). It has 11 vertices and 16 faces (15 equilateral triangles and 1 pentagon).
The gyroelongated pentagonal pyramid can be constructed by attaching a pentagonal pyramid to a pentagonal antiprism. It can also be constructed by deleting a single vertex from the icosahedron, and so can also be called the monodiminished icosahedron. It can be further diminished by removing a vertex not opposite the pentagonal face, producing a metabidiminished icosahedron (J62), or by removing two vertices, producing a tridiminished icosahedron (J63).
Projections
Here are some views of the gyroelongated pentagonal pyramid from various angles:
Projection  Envelope  Description 

Regular decagon  Top view. 

Pentagon  Side view. 

Pentagon  Front view. 
Coordinates
The Cartesian coordinates of the gyroelongated pentagonal pyramid with edge length 2 are:
 (0, 0, √((5+√5)/2))
 ±(B, 0, A)
 ±(C, ±φ, A)
 ±(−D, ±1, A)
where
A  =  √((5+√5)/10) 
B  =  √((10+2√5)/5) 
C  =  √((5−√5)/10) 
D  =  √((5+2√5)/5) 
φ  =  (1+√5)/2 