The molecular structures of Zr[(mu-H)(3)BH](4) and U[(mu-H)(3)BH](4) have been investigated by density functional theory (DFT) calculations and gas electron diffraction (GED). The triply bridged bonding mode of the tetrahydroborate groups in the former is confirmed, but both DFT calculations and GED structure refinements indicate that the BH(4) groups are rotated some 12 degrees away from the orientation in which the three bridging B-H bonds are staggered with respect to the opposing ZrB(3) fragment. As a result the symmetry of the equilibrium conformation is reduced from T(d) to T. Bond distances and valence angles are as follows (DFT/GED): Zr-B = 232.2/232.4(5) pm; Zr-H(b) = 214.8/214.4(6) pm; B-H(b) = 125.3/127.8(8) pm; B-H(t) = 119.4/118.8(17) pm; angle ZrBH(b) = 66.2/65.6(3) degrees; the smallest dihedral angle of type tau(BZrBH(b)) = 48/45(2) degrees. DFT calculations on Hf(BH(4))(4) indicate that the structure of this molecule is very similar to that of the Zr analogue. Matrix-isolation IR spectroscopy and DFT calculations on U(BH(4))(4) show that while the polymeric solid-state structure is characterized by terminal triply bridging and metal-metal bridging bidentate BH(4) groups, all BH(4) groups are triply bridging in the gaseous monomer. Calculations with one of the two nonbonding 5f electrons on U occupying an a(1) and the other distributed equally among the three t(2) orbitals indicate that the equilibrium conformation has T(d) symmetry, i.e. that the three B-H(b) bonds of each tetrahydroborate group are exactly staggered with respect to the opposing UB(3) fragment with tau(BUBH(b)) = 60 degrees. Calculations including spin-orbit interactions indicate that Jahn-Teller distortions from T(d) symmetry are either absent or very small. The best agreement between observed and calculated GED intensity data was obtained for a model of T(d) symmetry, but models of T symmetry with dihedral angles tau(BUBH(b)) > 42 degrees cannot be ruled out. Bond distances and valence angles are as follows (DFT/GED): U-B = 248.8/251.2(4) pm; U-H(b) = 227.7/231.5(6) pm; B-H(b) = 126.0/131.6(5) pm, B-H(t) = 119.5/117.8(11) pm; angle UBH(b) = 65.6/63.1(3) degrees. It is suggested that the different equilibrium conformations of the three molecules are determined primarily by repulsion between bridging H atoms in different tetrahydroborate groups.