The Gyroelongated Pentagonal Pyramid


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

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:

where

A=√((5+√5)/10)
B=√((10+2√5)/5)
C=√((5−√5)/10)
D=√((5+2√5)/5)
φ=(1+√5)/2

Last updated 18 Jun 2019.

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