Information below contains information that may ruin your enjoyment of discovering the game's secrets for yourself. Proceed at your own risk.
Geometric Triptychs are created within the Gateway Engines by placing a specific Resource in one of the three slots. Each planet requires a different resource to obtain the Geometric Triptych. The Gateway Engines can be activated with the corresponding Geometric Triptych created on that planet. The Triptychs can be used to activate spaces in the Gateway Portal, so the player can teleport from the respective planet to the Gateway Portal. All of the Triptychs are independent of each other, so not all of the Triptychs are needed to teleport to the Gateway Portal.
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Although the tooltip claims that it is "Embedded in a truncated pentachoron", this shape cannot be properly represented in three dimensions.