Johnson Solids (Page 1)

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(J9) Elongated Pentagonal Pyramid
Vertices:  11  (5[3] + 5[4] + 1[5])
Faces:11  (5 equilateral triangles + 5 squares + 1 regular pentagon)
Edges:20
Symmetry:  5-fold Pyramidal  (C5v)
(values below based on edge length = 1)
Volume:(5+sqrt(5)+6*sqrt(5*(5    
    +2*sqrt(5))))/24    
≈2.0219802329847914934