Yes they both have vertices
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Quadrilaterals, pentagons, triangles, octagons, hexagons, decagons.
An octahedron can have faces which are triangles, quadrilaterals, pentagons, hexagons or heptagons,
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 quadrilateral is a shape that has 4 sides, 4 angles, & 4 vertices.
A square and a rectangle