Acronym	peppy, 5pyr, J2
Name	pentagonal pyramid
	© ©   ©
Circumradius	sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figures	[35], [3,3,5]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dual	(topologically selfdual, in different orientation)
Dihedral angles	between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685° between {3} and {5}:   arccos(sqrt[(5+2 sqrt(5))/15]) = 37.377368°
Face vector	6, 10, 6
Confer	general pyramids: n/d-py   related Johnson solids: pedpy   gyepip   mibdi   teddi   aud   mabaud   pabaud   taud   uniform relative: ike   general polytopal classes: Johnson solids   segmentohedra   fundamental lace prisms
External links

As abstract polytope peppy is isomorph to stappy, thereby replacing the base pentagon by a pentagram.

This polyhedron is an edge-faceting of the icosahedron (ike).

Incidence matrix according to Dynkin symbol

ox5oo&#x   → height = sqrt((5-sqrt(5))/10) = 0.525731
(pt || {5})

tip  o. o.    | 1 * | 5 0 | 5 0
base .o .o    | * 5 | 1 2 | 2 1
--------------+-----+-----+----
lace oo5oo&#x | 1 1 | 5 * | 2 0
base .x ..    | 0 2 | * 5 | 1 1
--------------+-----+-----+----
coat ox ..&#x | 1 2 | 2 1 | 5 *
base .x5.o    | 0 5 | 0 5 | * 1