A 10.5 M☉ model of Population I composition is evolved from the main sequence through the core carbon-burning phase. As in 9 and 10 M☉ models studied in earlier papers of this series, carbon is ignited off center, but more carbon flashes occur before hydrogen is reignited and carbon burning dies out. Beginning with the second carbon flash, a carbon-burning flame propagates to the stellar center. The flame is divided into two parts by the flame "front" which is defined to coincide with the base of an associated convective shell. Ahead of the front is a "precursor" flame in which nuclear energy is converted into heat and the work of expansion at a rate comparable to the rate of release of nuclear energy in the convective shell. The width in mass of the precursor flame relative to the distance of the front from the center varies from ~0.01 when the front is at ~0.04 M☉ to ~1 as the front reaches ~10-7 M☉. Toward the end of the carbon-burning phase, the 10.5 M☉ model mixes helium- and carbon-rich matter with hydrogen-rich matter, but, in contrast to the other models, mixing does not occur across the base of a hydrogen-rich convective envelope which moves steadily inward through the helium-rich layer below it. Rather, a convective shell extending outward from the burning layers meets with the inward moving base of the convective envelope; then, hydrogen diffuses inward convectively and ignites as carbon and helium are diffusing outward through a region of variable composition. The luminous flux that forces convective motions at the base of the convective region is contributed to by carbon-burning, gravothermal, and helium-burning energy. The mixing process is modeled with a diffusion equation in which the diffusion coefficient is assumed to be a fraction of the local pressure scale height times a convective velocity that is estimated in the mixing-length approximation. When carbon burning dies out, the electron-degenerate core consists of an inner oxygen-neon (ONe) part of mass MONe ~ 1.263 M☉ in which 20Ne is more abundant than 12C, and an outer carbon-oxygen (CO) layer of mass ΔMCO ~ 0.0065 M☉ in which the reverse is true. Over most of the outer ~0.005 M☉ of the CO layer, the abundances of all neon isotopes is much less than 10-4 by number, and the number abundance of 25Mg and of other neutron-rich isotopes is equal to the total abundance of CNO elements in the initial main-sequence model. Final interior abundance characteristics in the deep interior of the ONe part of the core are very similar to those in the other models, the principal difference being that the maximum abundance by mass of 12C in the 10.5 M☉ model (X12 ~ 0.006) is significantly smaller than in the 10 M☉ model (X12 ~ 0.012) and in the 9 M☉ model (X12 ~ 0.048). This has ramifications for the question of the accretion-induced collapse of massive white dwarfs in cataclysmic variables and ultrasoft X-ray sources.