Looking at the fdisk output you posted I see 2 and not 3 partitions (/dev/sda1 and /dev/sda2). /dev/sda is the disk itself, and not a partition.
/dev/sda1 has a linux label and probably holds the basic linux system.
/dev/sda2 has a LVM label and is used as such.
The 2 /dev/mapper/... entries you see are LVM related. Both reside "inside" /dev/sda2 and that is why you only see 1 physical volume ("partition").
You might want to have a look at these links:
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Logical Volume Manager (Linux)
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Logical volume management
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Logical volume manager