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Rodinium (deteriorated from its normal state to be brittle)

Rodinium was one of the hardest known materials and it was frequently used in the construction of spacecraft and fixed installations. In 2266, rodinium was considered the hardest material known to Federation science, more than 21.4 times harder than diamond.

The Earth Outpost Stations along the Romulan Neutral Zone had armor made from cast rodinium, although that proved insufficient to protect them against the attack of a Romulan Bird-of-Prey's plasma torpedo. (TOS: "Balance of Terror")

Rodinium was also a common material in Cardassian starship construction. The debris analysis of the Bok'Nor found remnants of rodinium. (DS9: "The Maquis, Part I")

The figure for the hardness of rodinium comes from the hardness of tritanium, stated in the Star Trek: The Original Series episode "Obsession".
According to the Starfleet Medical Reference Manual (p. 18), the element rodinium, symbol Ro, atomic weight 323, atomic number 125, was first discovered on planet Vega IX.

Reality

In real-life science, element 125 has yet to be discovered or synthesized. A placeholder name based on its number, "unbipentium", has been suggested to document the possible existence of this element. Some models of theoretical science have stated that heavy elements on this scale may be impossible to synthesize or reproduce, and cannot exist in nature.

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