The Gyroelongated Pentagonal Pyramid

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The gyroelongated pentagonal pyramid is the 11th Johnson solid (J11). It has 11 vertices, 25 edges, 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