Use the buttons below each diagram to see a step-by-step walkthrough of each solution or explanation.
To get to the altar, you basically need to move counterclockwise around the temple, side-stepping into each of the three corners. The last corner aligns the gateways to provide a direct route to the altar.
The first sidestep is necessary to switch the alternating pattern of the gateways. Notice that trying to move clockwise around the temple, by going to the left at the entrance, is not possible because the gateways will always be closed.
The next sidestep into the corner is necessary to open the gateway into the main chamber.
Similarly, another sidestep is necessary to move to the other side of the main chamber. Moving around in the right side does not open the gateway in the central hallway, and if you try to move towards the altar, you will get trapped on the alpha tile.
In order to exit the temple, you need to move back to the right side of the main chamber, repeat your path back to the rear-left corner, and then continue moving counterclockwise, visiting the last of the four corners before exiting.
Why is all this necessary? First, you cannot leave the altar by turning right, since the gateways will always be closed.
Thus, you must leave the altar by turning left. Once in that section of the main chamber, you cannot leave directly through the adjoining hallway back to the entrance, since, any way you maneuver through that section, the gateways will be closed when you reach the beta tile.
Finally, in moving to the other side of the main chamber, if you attempt to go directly to the adjoining hallway back to the entrance, the gateways are in the wrong state to allow you to procede. The only way to fix this is to move to the rear-left corner, then return to the hallway back to the entrance.