Euphorbia polygona tends to be variable in form and appearance. At one stage of its botanical history under the name E. horrida it had four recognised varieties. This plant also tends to hybridize with some other members of its genus. Both of these features, variability and hybridisation, tend to complicate identification. The green fruit is a feature of some forms and ripening stages of the species; red brown and purple cyathia also vary.
The earlier horrida specific may be appropriate for the spiny aspect of the plant's appearance, but the pejorative element in naming is best avoided. Some of the spines are actually the stalks of the male and female cyathia that grow on separate plants (Euston-Brown and Kruger, 2023; Frandsen, 2017; Smith, et al, 2017; iNaturalist; www.cactus-art.biz).