The original description of Rebutia (Aylostera) iridescens was published in Kakteen und andere Sukkulenten 28(4): 76, 1977, the journal of the Deutsche Kakteen-Gesellschaft, by Friedrich Ritter.

Here is the text in Latin as published, followed by an English translation which is my own. You should look up the original description for more details.

Rebutia iridescens Ritter spec. nov.
Viridis, globosa, ad 4 cm crassa, radice rapaceae; costae ca. 10, crenatae, 4-6 mm altae; areolae 2-3 mm longae, ca. 1 mm latae, 4-7 mm inter se remotae, albolanatae; spinae 9-12, albidae, pulle acuminatae, lateraliter directae, 4-8 mm longae; interdum una centralis, longius.
Flores lateraliter positi, 35 mm longi ; ovarium abscure viridibus, lana alba et nonullis saetis albadis instructum; stylos cum tubo ca. 2-3 mm coalitus; camera nectarifera tubiformis, 4 mm longa; tubus floralis infundibuliformis, 8 mm longus; filamente viridia et rubida, 7 mm longa, biseriata; stylus viridis; stigmata 7, pallide viridia , 4 mm longa; petala 16-18 mm longa, 8-9 mm lata, spathulata, cinnabarina, rutile iridescentia; petala externa carmineopurpurea.

Habitat Mal Paso, Prov. Sud-Chichas, Bolivia.

Type species FR 1434.

English translation

Rebutia iridescens Ritter spec. nov.

Green, spherical, up to 4 cm thick, tap rooted; ca. 10 ribs, notched, 4 – 6 mm high; areoles 2 – 3 mm long, ca. 1 mm wide, 4 – 7 mm apart, white-wooled; 9 – 12 spines, whitish, dark at the tip, spreading sideways, 4 – 8 mm long; sometimes one longer central spine.

Flowers arising from the sides, 35mm long, ovary dull green with white wool and white bristles; style fused with flower tube for 2 – 3 mm, nectary tube 4 mm long; flowers funnel-shaped, 8 mm long; stamens green and dark purple, 7mm long, in two rows; style green; stigmas, 7, pale green, 4mm long; petals 16 – 18 mm long, 8 – 9 mm wide, spatulate, red (cinnabar), with golden-red iridescens; outer petals carmine-purple.

Habitat Mal Paso, Sud Chichas Province, Bolivia.

Type FR 1434.