Simple categories matching symmetrical:

• feature,
• container,
• object,
• shape,
• block,
• pearl,
• figure,
• structure,
• pattern,
• product,
• unit,
• model,
• stocking,
• part,
• form,
• symbol,
• organism,
• surface,
• item,
• trait,
• organs,
• motif,
• fashion,
• animal,
• creature,
• curve,
• solid,
• component,
• opening,

Members with property symmetrical:

• sphere,
• box,
• circle,
• clock,
• trapezoidal_solid,
• bookend,
• chair,
• cylinder,
• cnidarian,
• tree_structure,
• tube,
• model,
• game_ball,
• square,
• rectangle,
• optical_lense,
• ctenophore,
• ball,
• brain,
• tubular_crystal,
• nut,
• polygon,
• snowman,
• painted_vase,
• cube,
• broad_shoulder,
• snowflake,
• pipe,
• ellipse,
• reflector,
• regular_octahedron,
• disc,
• cocktail,
• piston,
• jellyfish,
• metal,
• octahedron,
• legs,
• vehicle_member,
• perfect_circle,
• tetrahedron,
• toy,
• bearing,
• ax,
• film,
• oblong_curve,
• zebra_stripe,
• round_sphere,
• human_brain,
• button,
• long_cylinder,
• hexagonal_shape,
• shield,
• fish_fin,
• envelope,
• torus,
• radial_pattern,
• disk-brake_disk,
• bolt,
• mollusc,
• rectangular_object,
• isosceles_triangle,
• drop,
• closure,
• bottle,
• spheroid,
• flower,
• impeller,
• auto,
• computer_equipment,
• tube_sock,
• rectangular_parallelepiped,
• rosette,
• hemisphere,
• book,
• round_disk,
• shaft,
• person,
• roller,
• earthworm,
• horizontal_stabilizer,
• mirror,
• arms,
• steps,
• coelenterate,
• virus_capsid,
• regular_dodecahedron,
• person_face,
• large_chest,
• concentric_pattern,
• drop_pearl,
• tweak_head,
• character,
• glass,
• octagon,
• cup,
• echinoderm,
• whole_body,
• concentric_circle,
• physical_system,
• shark,
• heart,
• cylindrical_cardboard,
• tails,
• cap,
• parallelepiped,
• bow,
• elongated_prism,
• human,
• paper,
• notebook,
• small_gear,
• boat,
• star,
• hexagon,
• stripe,
• bird,
• regular_polygon,
• teardrop,
• virus_particle,
• fcc_cube,
• old-fashioned_camera,
• truncated_cone,
• furniture,
• face,
• plane,
• dog,
• island_model,
• character_face,
• crayfish_great,
• ball_joint,
• cone,
• cylinder_shape,
• bolt_hole,
• dodecahedron,
• oval,
• annelid,
• drosophila,
• mouse,
• band,
• flat_disc,
• tree,
• triangle,
• turtle_deck,
• animal_head,
• spherical_sector,
• regular_hexahedron,
• fish,
• courthouse_steps,
• trapezoid,
• starfish,
• arrow,
• crystal,
• hole,
• plastic_elements,
• annulus,
• bulb_shape,
• stovepipe,
• fish_fig,
• ngf,
• eyes,
• rounded_rectangle,
• torso,
• apple,
• pentagon,
• axle,
• chicken,
• radiation,