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Algebra was not an important invention to Islam as a religion. It was an important invention in mathematics that was discovered by a Muslim (Al-Khwarizmi). Algebra is important in mathematics because it establishes the ability to perform mathematical operations even if some or all of the quantities are unknown.
It often represents the greatsness of Allah.
They can be, and are, cuboid. Cylindrical pillars are preferred because they do not have sharp corners.
Concrete with slabs of marble on the outside.
Not sure about a 5 digit word, but a 5 character word could be VITAL.