Bilunabirotunda (EntityTopic, 14)

From Hi.gher. Space

The bilunabirotunda is the 91st Johnson solid, J91. It suddenly became important when the castellated rhodoperihedral prism was discovered.

Coordinates

The following coordinates give an origin-centered bilunabirotunda with edge length 2:

<±1, 0, ±φ^2>

<±φ, ±1, ±1>

<0, ±φ, 0>

where φ=(1+√5)/2 is the Golden Ratio.

Equations

• The hypervolumes of a bilunabirotunda with side length l are given by:

total edge length = 26l
surface area = (2 + 2√3 + √(25+10√5)) · l²
volume = ¹∕₆ · (4φ² + 5φ) · l³