We investigate the structural, vibrational, and mechanical properties

of jammed packings of deformable particles with shape degrees of

freedom in three dimensions (3D). Each 3D deformable particle is

modeled as a surface-triangulated polyhedron, with spherical vertices

whose positions are determined by a shape-energy function with terms

that constrain the particle surface area, volume, and curvature, and

prevent interparticle overlap. We show that jammed packings of

deformable particles without bending energy possess low-frequency,

quartic vibrational modes, whose number decreases with increasing

asphericity and matches the number of missing contacts relative to the

isostatic value. In contrast, jammed packings of deformable particles

with non-zero bending energy are isostatic in 3D, with no quartic

modes. These studies underscore the importance of incorporating

particle deformability and shape change when modeling the properties

of jammed soft materials.