The 8-vertex unicursal deltahedra

The four unicursal deltahedra on eight vertices: (clockwise from upper left) Plantri numbers 8-0, 8-1, 8-3, 8-8.

The unicursal deltahedra on 8 vertices hold some distinction in that some are the smallest asymmetric unicursal deltahedra, and some give the first examples of the circle type face.

Here are all four of the unicursal deltahedra on 8 vertices by Plantri index, roadcode, stradcode, |Aut|, vertex-degree histogram, and number of vertex orbits in the dual.

8-0: |Aut|=1 Vdeg=[2 3 1 1 1] Vorb=12
2.11 13.0 14.9 5.18 20.7 15.22 10.23
1.24 25.12 26.3 28.17 6.29 19.30 31.4
32.27 33.16 21.34 8.35 
13.0+ 5.18+ -15.22 1.24- *25.12- 19.30+
o31.4+ -33.16 -21.34*

8-1: |Aut|=2 Vdeg=[2 2 3 0 1] Vorb=7
10.5 13.0 2.15 8.17 19.6 20.11 14.23
1.24 25.12 26.21 3.28 16.29 7.30 31.18
32.9 33.4 27.34 22.35 
13.0- 19.6+ 1.24- *25.12+ +3.28 7.30-
*31.18- -33.4 -27.34*

8-3: |Aut|=1 Vdeg=[3 1 2 1 1] Vorb=12
4.13 15.6 12.17 3.18 20.1 22.11 23.16
5.24 14.25 26.7 9.28 0.29 19.30 31.2
32.21 33.10 27.34 8.35 
+15.6 3.18- +23.16 +5.24o -9.28 19.30+
o31.2+ -33.10 -27.34*

8-8: |Aut|= 2 Vdeg=[1 3 3 1] Vorb=7
2.11 13.4 9.16 0.17 19.6 22.15 10.23
1.24 18.25 26.7 28.21 29.14 3.30 12.31
32.5 20.33 27.34 8.35
+13.4 -9.16+ +19.6- +1.24- -29.14 +3.30o
-27.34+

Three of these (8-0, 8-3, and 8-8) are cases where a unicursal deltahedron on 7 vertices has been augmented by a tetrahedron (tetrahedra are tricursal) and the result is unicursal. In these three cases the tetrahedron is joined to a minus type face, and the tetrahedron ends up wearing a circle type face that is adjacent to what had been the strad edge of the minus type face. In contrast, the 7-vertex shape tricorn has some faces of minus type, but attaching a tetrahedron to those faces evidently does not yield a unicursal result.