succulent, spineless, leafless; body or main stem short and thick, producing a crown of three or more series of crowded branches around the central flattened or depressed tuberculate obconic area at the top, and not rising much above ground level, tessellately tuberculate; branches 1 1/2–10 in. long or under cultivation much longer, 5–6 lin. thick, ascending or ascending-spreading, cylindric, tessellately tuberculate, glabrous, dull green; tubercles rhomboid, 2 1/2–5 lin. long, 1 3/4–2 3/4 lin. broad and 3/4 lin. prominent, shortly and obtusely conical, with a small white leaf-scar; leaves minute, rudimentary, soon deciduous, 1/2 lin. long and broad, ovate, acute; peduncles solitary in the axils of the tubercles at the tips of the branches, 1 1/2–2 lin. long, stout, bearing about 4 bracts and 1 involucre, glabrous, sometimes per-sistent; bracts 2/3–1 lin. long, scale-like, ovate or oblong, entire or ciliate; involucre 4–4 1/2 lin. in diam. (2 1/2–3 lin. when dried), cup-shaped, white, with 5 (rarely 4) glands and 5 transversely rectangular ciliate lobes, glabrous on the cup outside and within, but pubescent on the back of the lobes and filled with woolly-white bracteoles; glands glabrous, variable on the same plant, 1 1/4–1 1/2 lin. long, 1–1 1/2 lin. broad across the tips, sometimes ovate-oblong and very shortly bifid, with the lobes denticulate at the apex, sometimes divided to below the middle, with two diverging lobes cut like the horns of a reindeer, in both cases with the united glandular part dark green, revolute at the sides and the lobes white, sometimes divided nearly or quite to the base into 2 much-branched lobes and entirely white, without any glandular dark green part; ovary sessile, woolly-white at the apex, thinly sprinkled with ascending or spreading hairs or rarely glabrous; styles united to the apex into a slender column 1 1/2–2 lin. long; stigmas about 1/3 lin. long, more or less deeply bifid, with cuneate lobes, radiating and contiguous forming a sort of disc; capsule sessile, trigonous-subglobose, 2 1/2 lin. in diam., glabrous or with a few hairs; seeds 1 1/2 lin. long, ellipsoid, slightly 4-angled, subtruncate at the base, apiculate at the apex, very minutely tuberculate on the dorsal sides smooth on the ventral, dark brown, and (in the only example seen) with some whitish bodies (exudations?) at the angles, perhaps not constant. null