Elongated pentagonal pyramid

{{Infobox polytope The elongated pentagonal pyramid, or epeppy, is one of the 92 Johnson solids. It consists of 5 triangles, 5 squares, and 1 pentagon. It can be constructed by attaching a pentagonal pyramid to the base of the pentagonal pyramid..
 * type=CRF
 * img=Elongated pentagonal pyramid 2.png
 * 3d=J9 elongated pentagonal pyramid.stl
 * dim = 3
 * obsa = Epeppy
 * faces = 5 triangles, 5 squares, 1 pentagon
 * edges = 5+5+5+5
 * vertices = 1+5+5
 * verf = 1 pentagon, edge length 1; 5 kites, edge lengths 1 and $\sqrt{2}$; 5 isosceles triangles, edge lengths (1+$\sqrt{5}$)/2, $\sqrt{2}$, $\sqrt{2}$
 * coxeter = oxx5oo&#x
 * army=Epeppy
 * reg=Epeppy
 * symmetry = H2×I, order 10
 * volume = (5+$\sqrt{5}$+6$\sqrt{25+10)/24 ≈ 2.02198
 * dih = 3–3: acos(–√5/3) ≈ 138.18969º
 * dih2 = 3–4: acos(–√(10–2√5)/15) ≈ 127.37737º
 * dih3 = 4–4: 108º
 * dih4 = 4–5: 90º
 * dual = Elongated pentagonal pyramid
 * conjugate = Elongated pentagrammic pyramid
 * conv=Yes
 * orientable=Yes
 * nat=Tame}$

If a second pyramid is attached to the other base of the pentagonal prsm, the result is the elongated pentagonal bipyramid.

Vertex coordinates
An elongated pentagonal pyramid of edge length 1 has the following vertices:
 * (±1/2, –$\sqrt{(5+2√5)/20}$, ±1/2),
 * (±(1+$\sqrt{5}$)/4, $\sqrt{(5+√5)/40}$, ±1/2),
 * (0, $\sqrt{(5+√5)/10}$, ±1/2),
 * (0, 0, (1+$\sqrt{(5–√5)/10}$/2).