Bilunabirotunda (EntityTopic, 14)
From Hi.gher. Space
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The following coordinates give an origin-centered bilunabirotunda with edge length 2: | The following coordinates give an origin-centered bilunabirotunda with edge length 2: | ||
| - | :<±1, 0, ±φ | + | :<±1, 0, ±φ<sup>2</sup>> |
:<±φ, ±1, ±1> | :<±φ, ±1, ±1> | ||
:<0, ±φ, 0> | :<0, ±φ, 0> | ||
where φ=(1+√5)/2 is the Golden Ratio. | where φ=(1+√5)/2 is the Golden Ratio. | ||
| - | |||
== Equations == | == Equations == | ||
Revision as of 16:46, 16 February 2014
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, ±φ2>
- <±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
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
