Bilunabirotunda (EntityTopic, 14)

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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

Incidence matrix

Dual: J91 dual

#TXIDVaVbVcEaEbEcEdEe3a3b4a5aTypeName
0 Va = point ; cuboid corners
1 Vb = point ; crosses
2 Vc = point ; ends
3 Ea 200 = digon ; vertical cuboid
4 Eb 200 = digon ; horizontal cuboid
5 Ec 110 = digon ; cross-to-cuboid
6 Ed 101 = digon ; end-to-cuboid
7 Ee 002 = digon ; ends
8 3a 21010200 = triangle ; cross
9 3b 20101020 = triangle ; end
10 4a 40022000 = square ;
11 5a 21200221 = pentagon ;
12 C1a 824448824424 = bilunabirotunda ;

Usage as facets


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
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