  The first flavor-tagged amplitude analysis of the decay D0 to the
self-conjugate final state K+K-pi+pi- is presented. Data from the CLEO II.V,
CLEO III, and CLEO-c detectors are used, from which around 3000 signal decays
are selected. The three most significant amplitudes, which contribute to the
model that best fits the data, are phirho0, K1(1270)+-K-+, and non-resonant
K+K-pi+pi-. Separate amplitude analyses of D0 and D0-bar candidates indicate no
CP violation among the amplitudes at the level of 5% to 30% depending on the
mode. In addition, the sensitivity to the CP-violating parameter gamma/phi3 of
a sample of 2000 B+ -> D0-tilde(K+K-pi+pi-)K+ decays, where D0-tilde is a D0 or
D0-bar, collected at LHCb or a future flavor facility, is estimated to be (11.3
+/- 0.3) degrees using the favored model.
