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triple-fourth-cousin 

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents, zero great-great-grandparents and six great-great-great-grandparents in common.
Triple-fourth-cousin.

irregular-triple-fourth-cousin 

Someone who, in relation to others, has zero parents, zero grandparents, zero great-grandparents, zero great-great-grandparents and five great-great-great-grandparents in common.
Irregular-triple-fourth-cousin.