So, if you take a chart, and list every tribe once on each axis, you get 100 hybrids. 10 of these are original tribes, so 90 hybrids. Half of these are repeats, so we get 45 hybrids. Here is a list of all of them:
Mud/Sand, Mud/Sky, Mud/Sea, Mud/Rain, Mud/Ice, Mud/Night, Mud/Hive, Mud/Silk, Mud/Leaf
Sand/Sky, Sand/Sea, Sand/Rain, Sand/Ice, Sand/Night, Sand/Hive, Sand/Silk, Sand/Leaf
Sky/Sea, Sky/Rain, Sky/Ice, Sky/Night, Sky/Hive, Sky/Silk, Sky/Leaf
Sea/Rain, Sea/Ice, Sea/Night, Sea/Hive, Sea/Silk, Sea/Leaf
Rain/Ice, Rain/Night, Rain/Hive, Rain/Silk, Rain/Leaf
Ice/Night, Ice/Hive, Ice/Silk, Ice/Leaf
Night/Hive, Night/Silk, Night/Leaf
Hive/Silk, Hive/Leaf
Silk/Leaf