By considering the three-dimensional space of a regular tetrahedron, if from the center of the tetrahedron we draw a perpendicular to this 3-D space, every point of the perpendicular is equidistant to the four vertexes of the tetrahedron. The points on this line, whose distances to the four vertexes are equal to the edges of the tetrahedron, form with them a regular pentatope.
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