$(NH_4)_{4.5}[H_{3.5}{alpha}-PtMo_6O_{24}]{cdot}1.5;H_2O(A),;(NH_4)_4[H_4{eta}-PtMo_6O_{24}]{cdot}1.5;H_2O(B),;and;K_{3.5}[H_{4.5}{alpha}-PtMo_6O_{24}]{cdot}3;H_2O(C)$ have been synthesized and their molecular structures have been also determined by single-crystal X-ray diffraction technique. The space groups, unit cell parameters, and R factors are as follows: Compound A, monoclinic, $A_{2/a}$, a= 19.074 (3), b=21.490 (3), c=15.183 (2) ${AA};;{eta}$=109.67 (1) ${AA}$; z=8; R=0.075($IF_0I>4{sigma}(IF_0I);$ Compound B, triclinic, P$bar{1}$, a=10.776 (2), b=15.174 (4), c=10.697 (3) ${AA};;{alpha}$ =126.29 (2), ${eta}$=111.55 (2), ${gamma}$=93.18 (2) ${AA}$; Z=2; R=0.046($IF_0I>3{sigma}(IF_0I);$): Compound C, triclinic, Pl, a=12.426 (2), b=13.884 (2), c=10.089 (1) ${AA}$; ${alpha}$=102.59 (2), ${eta}$=110.73 (1), ${gamma}$=53.93 (1) ${AA}$; Z=2; R=0.074 ($IF_0I>3{sigma}(IF_0I)$. Compounds A and C contain the well-known Anderson structure (planar structure) heteropoly oxometalate having approximate $bar{3}_m(D_{3d})$ symmetry, while compound B contains the bent structure heteropoly oxometalate having appproximate $2_{mm}(C2_v)$ symmetry. The bent structure and the planar one are geometrical isomers. These compounds are rot only novel heteroply molybdates containing platinate(IV) but also the first example of geometrical isomerism in the hexamolybdoheteropoly oxometalates. That isomerization surprisingly occurred because of the change of only 0.5 non-acidic hydrogen atom attached to the polyanion such as $[H_{3.5}{alpha} -PtMo_6O_{24}]^{4.5-}{ o}[H_4{eta}-PtMo_6O_{24}]^{4-}{ o}[H_{4.5}{alpha} -PtMo_6O_{24}]^{3.5-}$. It seems that the gradual protonation of the polyanion plays an important role in that isomerism. These heteropolyanions form dimers by strong hydrogen bonds between two heteropolyanions in the respective crystal system.