hoof
蹄 centers on the hard, horny part of an animal's foot: a hoof. It is the specific body part that horses, cows, and similar animals walk on.
蹄 combines 足 (foot) with 帝, which likely contributes the sound. The character specifically denotes the hoof of an animal.
The left side 足 means foot, and the right side 帝 looks like a sturdy, horn-like shape. Picture an animal's foot ending in a hard, horny hoof.
For テイ, imagine a horse's hoof tapping on a table: the tap sounds like 'tei' (テイ), and the hoof is the foot that makes the sound.
hoof
horse's hooves
horseshoe
Tectus maximus (species of top shell)
Artiodactyla; order comprising the even-toed ungulates
artiodactyls; even-toed ungulates
hoof trimming; hoof cutting
Meridiungulata; extinct clade of South American ungulates
cloven foot
cloven-hoofed animal
foot-and-mouth disease; hoof-and-mouth disease
Perissodactyla (order of odd-toed ungulates, incl. horses, tapirs, etc.)
perissodactyls; odd-toed ungulates
ungulate; hoofed animal
ungulates
Japanese dock (Rumex japonicus)
shoeing a horse; horseshoeing
farrier (person who fits foot irons on horses and cows); hoof (care) specialist
frog; fourchette; pad in a horse's hoof that acts as a shock absorber
bulb (of an animal's hoof)