{"status": "success", "data": {"description_md": "Two distinct regular tetrahedra have all their vertices among the vertices of the same unit cube. What is the volume of the region formed by the intersection of the tetrahedra?\n\n$\\textbf{(A)}\\ \\frac{1}{12}\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{2}}{12}\\qquad\\textbf{(C)}\\ \\frac{\\sqrt{3}}{12}\\qquad\\textbf{(D)}\\ \\frac{1}{6}\\qquad\\textbf{(E)}\\ \\frac{\\sqrt{2}}{6}$", "description_html": "<p>Two distinct regular tetrahedra have all their vertices among the vertices of the same unit cube. What is the volume of the region formed by the intersection of the tetrahedra?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{12}\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{2}}{12}\\qquad\\textbf{(C)}\\ \\frac{\\sqrt{3}}{12}\\qquad\\textbf{(D)}\\ \\frac{1}{6}\\qquad\\textbf{(E)}\\ \\frac{\\sqrt{2}}{6}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2011 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc10A_p25", "prev": "/problem/11_amc10A_p23"}}