How does USB Type C handle reverse polarity / signal duplication
Below is the pinout for the receptacle:

GND  TX1+ TX1- Vbus CC1   D+   D-  SBU1 Vbus RX2- RX2+ GND
 |    |    |    |    |    |    |    |    |    |    |    |
=+====+====+====+====+====+====+====+====+====+====+====+=
 |    |    |    |    |    |    |    |    |    |    |    |
GND  RX1+ RX1- Vbus SBU2  D-   D+  CC2  Vbus TX2- TX2+ GND


You will note that all the pins are rotationally symmetric, so if you flip the connector, TX1+ connects to TX2+, TX1- connects to TX2-, etc. and most importantly, Vbus and GND always match up.

The trick lies in the controller and cable -- the CC pins are used to detect orientation, at which point the controller routes appropriately:


  2.3.2 Plug Orientation/Cable Twist Detection
  
  The USB Type-C plug can be inserted into a receptacle in either one of two orientations, therefore the CC pins enable a method for detecting plug orientation in order to determine which SuperSpeed USB data signal pairs are functionally connected through the cable. This allows for signal routing, if needed, within a DFP or UFP to be established for a successful connection.





As you might imagine, the cables are going to be a fair bit heftier due to the extra wires.


A minimum of 15 wires plus braid required for full-featured Type-C (i.e. USB 3.1 -- recommended 4-6mm outer diameter)
10 wires plus braid for legacy Type-C USB 3.0/3.1 cables (intended to connect to Type-A or Type-B on the other end -- recommended 3-5mm outer diameter)
For USB 2.0 or earlier, whether connecting to Type-C or a legacy type on the other end, the usual four wire configuration is permitted (recommended 2-4mm outer diameter)


Source: USB 3.1 Specification @ usb.org -- specifically, the Universal Serial Bus Revision 3.1 Specification PDF available for download at the top of the page)

Also a great blog post explaining all the details about the Configuration Channel pin:

http://kevinzhengwork.blogspot.de/2014/09/usb-type-c-configuration-channel-cc-pin.html

Archive.org (in case it goes offline)