Known as The Pyramid Temple, it was part of the corrupted Gem's form, rather than a structure that Homeworld Gems managing to build a temple during the midst of war, when (in It Could've Been Great) it has been shown that the rebellion had managed to halt Homeworld's building projects on Earth. There is a structure on Earth that is not listed on the Moon Base and bears the Era 2 logo. Currently it has no name but it is likely to be called Era 2. Peridot's words also implies that there is more than one era, so it is likely that the newer (triangular) Homeworld logo refers to the era after Era 1, after Pink Diamond's removal from the Great Diamond Authority. It is likely that the old Homeworld Symbol actually refers to what Homeworld Gems call "Era 1" - which would be the time when there were four Diamonds. These Gem structures bear the old Homeworld symbol. We know from "It Could've Been Great" that the Kindergarten dated from the time when other Gem structures such as the Lunar Sea Spire and the Moon Base were created. In "Too Far" Peridot describes the Kindergarten's injectors as being Era 1 ones. The missing colour is pink, which is often refered by people as a Diamond that was removed from the Great Diamond Authority - Pink Diamond. The colours correspond to three of the four Diamonds that were referenced in the first Homeworld logo.
The second logo is comprised of three coloured triangles in a triangular arangement. The first logo which is associated with Gem constructions prior to the Rebellion (Gem Wars) has four different coloured diamonds, with each one representing one of the four Diamond matriarchs that govern Homeworld and its other Gem colonies.
It has been pointed out that Homeworld Gems have two similar logos for their Great Diamond Authority. This theory is an attempt to shed light on the two seperate eras of Homeworld history which are marked by the changes to their Great Diamond Authority, as well as the actual names given by Homeworld Gems to reference these times.