This page shows 90%-symmetric solutions.
The solids are placed along the top edge, corners and middle.
Green is symmetric with itself, and blue with red.
In each solution, just six segments are asymmetric.
1.-4.: 56-62 with 57-63, 70-71, 92-93, 100-106 with 101-107.
5.-6.: 56-62 with 57-63, 78-84 with 79-85, 92-93, and 114-115.
7.-10.: 2-3 with 6-7, 68-69 with 72-73, 92-93, and 114-115.