A combination of experiment and theory provides insight into the structure and rearrangements of various C3H2 isomers. Photolysis of [C-13]diazopropynes 6a-c under matrix isolation conditions affords C3H2 isomers containing a single C-13-label. With the aid of computed vibrational frequencies and intensities (CCSD(T)/cc-pVTZ), the seven C-13-isotopomers of triplet propynylidene 1a,b, singlet propadienylidene 2a-c, and singlet cyclopropenylidene 3a,b are readily distinguished by LR spectroscopy. Monitoring the distribution of the C-13-label during photolysis at either lambda = 313 +/- 10 nm or lambda > 444 nm reveals the involvement of two photochemical automerization processes. At lambda = 313 +/- 10 nm, triplet propynylidene and singlet cyclopropenylidene photoequilibrate. The interconversion does not occur by a simple ring closure/ring opening mechanism, as hydrogen migration accompanies the interconversion. At lambda > 444 nm, H2C=C=C-13 : (2b) and H2C=C-13=C : (2c) rapidly equilibrate. Various lines of evidence suggest that the equilibration occurs through a cyclopropyne transition state. Computational results confirm that the planar isomer of singlet cyclopropyne (4a, C-2v) is the transition state for the interconversion of 2b and 2c. Unexpectedly, the calculations predict that the isomer of this compound containing a tetrahedral carbon atom (4b, C-2v) lies ca. 7 kcal/mol higher in energy than the planar form.