molecular geomatry shape of h2c2o4?

H₂C₂O₄ do not have fixed shape because the C-C single bond can rotate.

However, for each C atom as the central atom, it is trigonal planar.

The diagram below shows three of the many shapes of H₂C₂O₄.

H2C2O4 .... oxalic acid ..... HOOC-COOH

It would make more sense to ask about the geometry about each carbon atom. Since each carbon has three bonding pairs (sigma bonds) and no lone pairs, then it is trigonal planar, as indicated by VSEPR theory. The fourth bond on carbon is a pi bond and completes the double bond to an oxygen.

O.......... O
..\\....... //
...C − C
.../........\
.OH......OH

VSEPR Theory
#electron pairs ..... e- pair geom..... molecular geom..... bond angle
2 ........................... linear ..................... linear .................... 180
3 (no lone pairs) .. trigonal planar ...... trigonal planar ....... 120
3 (one lone pair) .. trigonal planar ...... bent .........................LT 120
4 (no lone pairs) .. tetrahedral ............ tetrahedral .............. 109.5
4 (one lone pair) .. tetrahedral ............ trigonal pyramidal .. LT 109.5
4 (2 lone pairs) .... tetrahedral ............ bent ...................….. LT. 109.5
5 (no lone pairs) .. trig bipyramidal ....trig bipyramidal ….. 90 and 120
5 (one lone pair) .. trig bipyramidal ... see-saw ................... 90 and 120
5 (2 lone pairs) .... trig bipyramidal ....T-shaped .............,... 90
5 (3 lone pairs) .... trig bipyramidal ....linear ........................180
6 (no lone pairs) .. octahedral ............ octahedral ................ 90
6 (one lone pair) .. octahedral ............ square pyramidal ......90
6 (2 lone pairs) .... octahedral ............ square planar .............90
(LT = "less than")

Probably best posted over in Chemistry vs Math. I'll attempt a move.

I think: H2C2O4 is oxalic acid. HOC(=O)-C(=O)-OH
all carbons are SP2 hybridized planar. In fact all atoms are planar.