The Bigyrate Diminished Rhombicosidodecahedron


The bigyrate diminished rhombicosidodecahedron is the 79th Johnson solid, or J79 for short. It has 52 faces (1 decagon, 11 pentagons, 25 squares, and 15 triangles), 105 edges, and 55 vertices. It is obtained by cutting off a pentagonal cupola segment from the rhombicosidodecahedron and gyrating two oblique pentagonal cupola segments.

A bigyrate diminished
rhombicosidodecahedron

The bigyrate diminished rhombicosidodecahedron closely resembles the diminished rhombicosidodecahedron (J76), but can be distinguished from the latter by telltale pairs of adjacent squares, which are not present in J76:

A bigyrate diminished
rhombicosidodecahedron, highlighting pairs of adjacent squares

It can also be distinguished from also very similar J77 and J78 by the strip of 3 adjacent squares unique to the metabigyrates of the rhombicosidodecahedron, highlighted in yellow below:

A bigyrate diminished
rhombicosidodecahedron, highlighting pairs of adjacent squares

These pairs of adjacent squares and strip of 3 adjacent squares occur because of the gyrated orientation of the two pentagonal cupola segments highlighted below:

A bigyrate diminished
rhombicosidodecahedron, highlighting gyrated cupola segments

Projections

Here are some views of the bigyrate diminished rhombicosidodecahedron from various angles. For ease of reference, we highlight the strip of 3 squares in yellow.

Projection Description

Top view.

Front view.

Side view.

Oblique side view.

Coordinates

The Cartesian coordinates of the bigyrate diminished rhombicosidodecahedron with edge length 2 are:

where φ=(1+√5)/2 is the Golden Ratio.


Last updated 21 May 2019.

Powered by Apache Runs on Debian GNU/Linux Viewable on any browser Valid CSS Valid HTML 5! Proud to be Microsoft-free