The most common geometry for Tanto has hira zukuri.
Thickness starts at around 3mm-4mm.
Traditional Hira zukuri has a very convexed edge with a lot of Niku (meat). A flat back was actually not common at all, and has only been found on ancient blades (we're talking very very old). More then likely Iori-mune, and Mitsu mune would have been the most common mune (spines). Iori mune is a triangle shape and would have likely been the most common while Mitsu mune has three surfaces, two of them are angled to join but then the 3rd surface stops it kind of like a flat peaked mountain and would have been one of the least common types of mune.
Not all geometries were present in tanto, I have my book here with me. (same one linked by Hesparus).
Kissaki-Moroha-zukuri for example, I don't believe an example exists or existed in tanto form. Or at least I dont think it was documented.
There's maybe one geometry that was not present in katana, that's Osoraku-zukuri. Only seen in Tanto and wakizashi.