I found two papers from which two different formulae for the tetrasilicate (tetrasilicic acid) are found:

Of course, the usual formula for polymerization of oxacids suggest the first one is the right one, that is, the tetrasilicate anion being $$\ce,{Si_4O_9^{2-}}$$, however, how to understand the second formula? Is something missing?

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• First you mention is cyclic, second linear, probably tetracyclic "tetrahedron of tetrahedra" also exists. – Mithoron Dec 7 '18 at 22:18
• Yeah, but why? I believed the polymerized oxacid tetrasilicic acid had only a single formula... – riemannium Dec 7 '18 at 22:26
• "tetrasilicic acid" in not a unique name. SiO4 tetrahedra may be connected in as many ways as possible. – Mithoron Dec 7 '18 at 22:36
• Polymerization: n(oxoacid)-(n-1)$$H_2O$$. That is why I got surprised... – riemannium Dec 7 '18 at 22:42
• – Mithoron Dec 8 '18 at 0:14

"Tetrasilicate" is one of special guys. For example, sulfate is $$\ce{SO_4^2-}$$, while $$\ce{SO_3^2-}$$ is sulfite. But tetrasilicate is $$\ce{Si_4O_n^{(2n-16)-}}$$ - thus, it simply has four $$\ce{Si}$$ atoms (without connotation that they have special number of oxygens near 'em): check for

http://www.biomedsearch.com/nih/Novel-silicate-anion-Si8O2212-Hydrothermal/11487344.html, which is also tetrasilicate (here tetrasilicate is $$\ce{Si_4O_11^6-}$$).

https://www.researchgate.net/publication/50934696_Preparation_structural_and_luminescent_properties_of_Ba2Gd2Si4O13Eu3_for_white_LEDs (tetrasilicate is $$\ce{Si_4O_13^10-}$$), etc.

[edited] I've found for you even tetrasilicate with 15 oxygens: https://link.springer.com/article/10.1007/s00710-016-0447-1

Also check for amicite (zeolite): it has approximation $$\ce{K2Na2Al4Si4O16·5(H2O)}$$. It seems for me like 16 oxygens is maximum for tetrasilicates, but maybe someone would disagree - interesting to know that other tetrasilicates exist.

• How many special "guys" similar to tetrasilicates are out there? Wonderful! – riemannium Dec 7 '18 at 22:11
• Pretty many.$\,$ – Ivan Neretin Dec 8 '18 at 8:02
• Examples out there? – riemannium Dec 13 '18 at 0:31