<Tr> <Td> Regular tetrahedron of side s and mass m </Td> <Td> </Td> <Td> I s o l i d = 1 20 m s 2 (\ displaystyle I_ (\ mathrm (solid)) = (\ frac (1) (20)) ms ^ (2) \, \!) <P> I h o l l o w = 1 12 m s 2 (\ displaystyle I_ (\ mathrm (hollow)) = (\ frac (1) (12)) ms ^ (2) \, \!) </P> </Td> </Tr> <P> I h o l l o w = 1 12 m s 2 (\ displaystyle I_ (\ mathrm (hollow)) = (\ frac (1) (12)) ms ^ (2) \, \!) </P> <Tr> <Td> Regular octahedron of side s and mass m </Td> <Td> </Td> <Td> I x, h o l l o w = I y, h o l l o w = I z, h o l l o w = 1 6 m s 2 (\ displaystyle I_ (x, \ mathrm (hollow)) = I_ (y, \ mathrm (hollow)) = I_ (z, \ mathrm (hollow)) = (\ frac (1) (6)) ms ^ (2) \, \!) I x, s o l i d = I y, s o l i d = I z, s o l i d = 1 10 m s 2 (\ displaystyle I_ (x, solid) = I_ (y, solid) = I_ (z, solid) = (\ frac (1) (10)) ms ^ (2) \, \!) </Td> </Tr> <Tr> <Td> Regular dodecahedron of side s and mass m </Td> <Td> </Td> <Td> I x, h o l l o w = I y, h o l l o w = I z, h o l l o w = 39 φ + 28 90 m s 2 (\ displaystyle I_ (x, \ mathrm (hollow)) = I_ (y, \ mathrm (hollow)) = I_ (z, \ mathrm (hollow)) = (\ frac (39 \ phi + 28) (90)) ms ^ (2)) <P> I x, s o l i d = I y, s o l i d = I z, s o l i d = 39 φ + 28 150 m s 2 (\ displaystyle I_ (x, \ mathrm (solid)) = I_ (y, \ mathrm (solid)) = I_ (z, \ mathrm (solid)) = (\ frac (39 \ phi + 28) (150)) ms ^ (2) \, \!) (where φ = 1 + 5 2 (\ displaystyle \ phi = (\ frac (1 + (\ sqrt (5))) (2)))) </P> </Td> </Tr>

Moment of inertia of a rod with a mass on it