Euphorbia braunsii, previously E. rudis , is a sturdy stem succulent growing stout, cylindrical branches above a thick, underground rootstock and short stem to heights around 25 cm and width of 35 cm. The outer branches are continually forced further outwards by new ones emerging in the centre. A mature plant forms a near hemisphere as in the photo, eventually touching the ground. This is one of the vingerpol type euphorbias that also bears that name.
Some dry stalks, the peduncles of cyathia that were on the stem tops of the younger plant when the stems had been much shorter, are present below the leaves on the branches in picture. This is not really a spiny species, the irregularly shaped “flower” stalks being sparsely distributed.
The species distribution is in the Northern Cape and the Western Cape as far east as Beaufort West and Prince Albert.
The habitat is stony flats of succulent Karoo and Nama Karoo where the soil is loamy. The species is not considered threatened in habitat early in the twenty first century (Frandsen, 2017; Williamson, 2010; iNaturalist; iSpot; JSTOR; http://redlist.sanbi.org).