  Within the low-lying spectrum of 10Be, multiple rotational bands are found,
with strikingly different moments of inertia. A proposed interpretation has
been that these bands variously represent triaxial rotation and prolate
axially-deformed rotation. The bands are well-reproduced in ab initio no-core
configuration interaction (NCCI) calculations. We use the calculated wave
functions to elucidate the nuclear shapes underlying these bands, by examining
the Elliott SU(3) symmetry content of these wave functions. The ab initio
results support an interpretation in which the ground-state band, along with an
accompanying K=2 side band, represent a triaxial rotor, arising from an SU(3)
irreducible representation in the 0 hbar omega space. Then, the lowest excited
K=0 band represents a prolate rotor, arising from an SU(3) irreducible
representation in the 2 hbar omega space.
