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an angle
It means 'joined to'. The 'school's adjoining building' is 'the building that is joined to the school'.
A pentagonal heptahedron is a heptahedron comprising two pentagons which are joined to one another by five quadrilaterals. There is no requirement for the pentagons to be congruent nor for them to be parallel to one another.
A clause is a sort of sentence within a sentence. In some cases they can be joined together with conjunctions such as or, and or but. For example: He put on his coat and they walked to the beach. "He put on his coat" is one clause and "They walked to the beach" is another. Because they do not depend on one another and are joined by a coordinating conjunction (the word and) such clauses are referred to as coordinate clauses.
A polygon is a shape joined together by 3 or more lines such as a triangle, a quadrilateral, a pentagon, an hexagon ..... etc