Archimedean-Catalan Hulls
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Joined Rhombicuboctahedron
Vertices:
50 (8[3] + 24[4] + 12[4] + 6[4])
Faces:
48 (24 kites + 24 rhombi)
Edges:
96 (24 short + 72 long)
Symmetry:
Full Octahedral (Oh)
Long Edge Angle:
acos(−(2+sqrt(2))/4)
≈148.600285190 degrees
Short Edge Angle:
acos(−(6+sqrt(2))/8)
≈157.937808842 degrees
(values below based on unit-edge-length
Rhombicuboctahedron
)
Short Edge (24):
sqrt(69−2*sqrt(2))/14
≈0.58104222367231665644
Long Edge (72):
sqrt(5−2*sqrt(2))/2
≈0.73681287910395029658
Rhombus Length:
sqrt(2*(2−sqrt(2)))
≈1.0823922002923939688
Rhombus Width:
1
Kite Length:
2*sqrt(10−sqrt(2))/7
≈0.83718607580427642316
Kite Width:
1
[3]-Vertex Radius (8):
(4*sqrt(3)+sqrt(6))/7
≈1.3396704247226696103
[4]-Vertex Radius (24):
sqrt(5+2*sqrt(2))/2
≈1.3989663259659067020
[4]-Vertex Radius (12):
sqrt(2)
≈1.4142135623730950488
[4]-Vertex Radius (6):
sqrt(2)
≈1.4142135623730950488
Inscribed Radius:
sqrt(2*(2+sqrt(2)))/2
≈1.3065629648763765279
Volume:
4*(2+11*sqrt(2))/7
≈10.0321995349165974496
References:
[1]
Conway Notation for Polyhedra (George Hart)