Skeleton Pentominoes #2

Normal sudoku rules apply.

Digits on thermometers should increase from the bulb end.

Shade some cells such that the resulting pattern is 90-degree rotationally symmetric. For example, if r3c1 is shaded, then so are r1c7, r7c9, and r9c3.

The unshaded region must contain one each of the twelve standard pentominoes (no repeats by rotation or reflection).

Each pentomino encloses exactly one caged cell and one thermometer.

The arrangement of pentominoes must be deduced.

Once placed, the pentominoes can be shaded with just 3 colors, such that no two pentominoes of the same color touch each other orthogonally or diagonally. All pentominoes of the same color contain a digit in common that lives in the caged cell. For one group the digit is 1, the next group 5, and the last group 9.

Additionally, each pentomino behaves like a 5-cell killer cage: digits do not repeat and must sum to the clue in the corner of the caged cell.

Illustrated Pentominoes at: https://tinyurl.com/pent-labels