Clock face broken into three equal-sum pieces

A clock face shatters into three pieces, and the hour numbers on each piece add up to the same total. Which numbers are on each piece?

$\{11,12,1,2\}$, $\{10,9,3,4\}$ and $\{5,6,7,8\}$. The numbers $1$ to $12$ sum to $78$, so each piece totals $26$. Two roughly horizontal cuts, one between $10$/$11$ and $2$/$3$ and one between $8$/$9$ and $4$/$5$, produce these three bands.