The Gyroelongated Pentagonal Cupolarotunda


The gyroelongated pentagonal cupolarotunda is the 47th Johnson solid (J47). It has 35 vertices, 80 edges, and 47 faces (35 equilateral triangles, 5 squares, and 7 pentagons).

The gyroelongated
pentagonal cupolarotunda

The gyroelongated pentagonal cupolarotunda can be constructed by attaching a pentagonal rotunda and a pentagonal cupola to a decagonal antiprism, or equivalently, adding a pentagonal rotunda to a gyroelongated pentagonal cupola (J24), or adding a pentagonal cupola to a gyroelongated pentagonal rotunda (J25).

J47 is one of the few Johnson solids that are chiral; it is distinct from its own mirror image:

One enantiomorph of the
gyroelongated pentagonal cupolarotunda The
other enantiomorph of the gyroelongated pentagonal cupolarotunda

Projections

Here are some views of the gyroelongated pentagonal cupolarotunda from various angles:

Projection Description

Top view.

Front view.

Side view.

9° side view.

Coordinates

The Cartesian coordinates of the gyroelongated pentagonal cupolarotunda with edge length 2 are:

where H = √(√(11φ+7)−2φ−1), approximately 0.862397, is half the height of a decagonal antiprism of edge length 2, and φ = (1+√5)/2 is the Golden Ratio.


Last updated 19 Jun 2018.

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