We report the results of systematic experimental and theoretical studies of two closely related species of magnetic molecules of the type

{V_{6}},

where each molecule includes a pair of triangles of exchange-coupled vanadyl

({VO}^{2 +},

spin

s = 1 / 2)

ions. The experimental studies include the temperature dependence of the low-field susceptibility from room temperature down to 2 K, the dependence of the magnetization on magnetic field up to 60 T for several low temperatures, the temperature dependence of the magnetic contribution to the specific heat, and the

^{1} H

and

^{23} Na

nuclear magnetic resonance spin-lattice relaxation rates

{1 / T}_{1} .

This body of experimental data is accurately reproduced for both compounds by a Heisenberg model for two identical uncoupled triangles of spins; in each triangle, the spins interact via isotropic antiferromagnetic exchange, where two of the three V-V interactions have exchange constants that are equal and an order of magnitude larger than the third; the ground-state eigenfunction has total spin quantum number

S = 1 / 2

for magnetic fields below a predicted critical field

H_{c} \approx 74 T

and

S = 3 / 2

for fields above

H_{c} .

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