Archimedean-Catalan Hulls

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

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)