Oct has 4 edge facetings, each with its own symmetry. All are tame and legit (not fissary). All are orientable except for thah.
1. Oct - (OCT / octahedron). It has 8 trigs and has cubic symmetry and is regular. It has only one orientation.
2. Thah - (THAH / tetrahemihexahedron). It has 4 trigs and 3 squares. It is uniform and has tettic symmetry. Two possible orientations.
3. Squippy - (SQUIP pee / square pyramid) It has 4 trigs and 1 square. It has squippyric symmetry, it is a Johnson solid with six possible orientations, two having the same symmetry.
4. Bobipyr - (BOB ih pur / bowtie bipyramid) It has 4 trigs and 2 squares. It has brick symmetry. It is also called bowtie tegum (bot). It has six possible orientations, with two with the same symmetry.
Co has 7 edge facetings, 3 are uniform with cubic symmetry, 2 have trippyric symmetry, and 2 have brick symmetry. All are legit and tame.
1. Co - (CO / cuboctahedron). It has 6 squares and 8 trigs. It has cubic symmetry and is uniform and orientable. It has one orientation.
2. Oho - (O ho / octahemioctahedron). It has 8 trigs and 4 higs. It has cubic symmetry and is uniform and orientable. It has one orientation.
3. Cho - (CHO / cubihemioctahedron). It has 6 squares and 4 higs. It has cubic symmetry and is uniform and non-orientable. It has one orientation.
4. Tricu - (TRIK cue / triangular cupola). It has 1+3 trigs, 3 squares, and 1 hig. It has trippyric symmetry and is a Johnson solid. It is orientable and has eight orientations with two having the same symmetry.
5. Gripper - (GRIP per / gripper). It has 1+3 trigs, 3 squares, and 3 higs. It has trippyric symmetry and is non-orientable. It has eight orientations with two having the same symmetry.
6. Ebot - (E bot / elongated bowtie tegum) It has 4 trigs, 2 squares, and 2 higs. It has brick symmetry and is orientable. It has six orientations with two having the same symmetry.
7. Bocuco - (bo KU ko / bowtie cut cuboctahedron) It has 4 trigs, 4 squares, and 2 higs. It has brick symmetry and is orientable. It has six orientations with two having the same symmetry.
Conjugates
The following are self conjugates: all.
The following are conjugate pairs: none.
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