The female paratypes ranged from 22 mm to 33 mm in length, and the male holotype measured 26 mm in length. The female paratypes had 24 or 25 pairs of legs, whereas the male holotype had 23 leg pairs. The background color of the body in living specimens is a dark grayish red. The jaw features two blades, an inner blade and an outer blade, each with a long curved main tooth and one accessory tooth. In the male of this species, one or two pairs of the pregenital legs feature crural papillae (tubercles), with one papilla per leg.[1][4]
The largest primary papillae are pale, and the number of these pale primary papillae increases near the legs. The basal piece of the primary papillae features six or seven scale ranks. The apical piece is robust and spherical, but with an asymmetric distribution of scales: six or seven scale ranks in the front and three in the back. A needle-shaped sensory bristle emerges from the back side of the apical piece.[1]
This species exhibits traits considered diagnostic for the genus Epiperipatus. These traits include the number of pregenital legs with crural papillae in males and the number of scale ranks at the base of the primary papillae. Furthermore, like other species in this genus, this species features nephridial tubercles on the fourth and fifth leg pairs, with each tubercle located between the third and fourth spinous pads on the soles of the feet.[1][3][4]
This species shares a more extensive set of traits with its close relatives, E. titaniccus and E. lucerna. For example, all three species exhibits the same dorsal background color and the same arrangement of pale primary papillae. Furthermore, all three species feature one accessory tooth in addition to the main tooth on both the inner and outer jaw blades. Moreover, the males of each species feature pregenital legs with crural papillae, with one crural papilla per leg.[1]
These three species can be distinguished, however, by the apical piece of their primary papillae. In E. hyperbolicus, this piece is large and spherical, with an asymmetric distribution of scales: six or seven scale ranks in the front and three in the back. In E. titanicus, this piece is conical with a symmetric distribution of scales, which are reduced to one rank. In E. lucerna, this piece is also conical, but with an asymmetric distribution of scales: three scale ranks in the front and two in the back. Furthermore, E. hyperbolicus features fewer legs (23 to 25 pairs) than either E. lucerna (27 to 31 pairs) or E. titanicus (36 to 39 pairs).[1]