Perhaps we can expand the key for woody succulent species of Euphorbia as under:
Stems unarmed; without stipular spines
Leaves shorter than 10 cm, uniformally green
Stem and leaves uniformly red, leaves in whorls of three, petiole almost as long as blade...............................................E. cotoniifolia
Stem and leaves green, leaves alternate, petiole much shorter than blade
Leaves shorter than 2 cm, less than 2 mm broad, branches straight, mostly leafless (leaves early deciduous).............E. tirucalli
Leaves longer than 3 cm, more than 2 cm broad, branches zigzag, mostly with leaves..............................................E. tithymaloides
Leaves longer than 10 cm; uniformally or partly coloured
Leaves below the inflorescence uniformally coloured (red, white or yellow); leaves not lobed.......................................E. pulcherrima
Leaves below the inflorescence coloured only at base; leaves lobed or not
Base of upper leaves pale green or pale white; leaves lobed or not.......................................................................E. heterophylla
Base of upper leaves red; leaves lobed..............................................................................................................E. cyathophora
Stems armed with spines
Spines borne on stem, usually longer than 1 cm...............................................................................................................E. milii
Spines borne on raised shield, usually shorter than 1 cm
Stem rounded, not angled or winged
Shrub wiithout trunk with branches arising from base, smaller leaves (3-8 cm long) and longer spines 0.5-1 cm.................E caducifolia
Tree with distinct trunk, leaves 10-25 cm long, spines shorter than 0.5 cm.......................................................................E. nivulia).
Stem angled or winged
Angles not produced into wing, spirally arranged:...................................................................................................... E. neriifolia
Angles produced into wings
Wings 3-4
The wings running straight, sinuate, regularly dentate
Stems green without white bands..........................................................................................:........E. antiquorum
Stems white wholly or partially
The stems with white bands on faces
Apex of stem not cristate (without crowns at tips).........................................................E. lactea
Apex of stem cristate (with crowns at tips)....................................................................E lactea cv. Cristata
The stems uniformly greyish white.......................................................................................E. lactea cv. White Ghost
The wings running spirally, ................................................................................................................................E. tortilis
Wings 5-6, undulate..................................................................................................................................................E. royleana