Assertion: tetrahedron | /r/HasProperty | abcd
Facets:
Source sentences:
text: Another characterization states that if d 1 , d 2 and d 3 are the common perpendiculars of AB and CD; AC and BD; and AD and BC respectively in a tetrahedron ABCD, then the tetrahedron is a disphenoid if and only if d 1 , d 2 and d 3 are pairwise perpendicular.
text: If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron AB CD is formed so that its edge AB represents the tension of the surface of contact of the liquids a and b, BC that of b and c, and so on; then if we place this tetrahedron so that the face ABC is normal to the tangent at 0 to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at 0 to the surface of contact of the fluids a and b, then the other three faces of the tetrahedron will be normal to the tangents at 0 to the other three lines of concourse of the liquids, an the other five edges of the tetrahedron will be normal to the tangent planes at 0 to the other five surfaces of contact.
text: Let us consider the tetrahedron ABCD as above, for our further discussions, with BCD as the base triangle and A as the peak point.
text: Two triangles ADB and ADC, with AD as the common edge, and Φbc as the dihedral angle between them, can fully describe the tetrahedron ABCD.
text: Using this, for a tetrahedron ABCD we can write,
text: Consider a tetrahedron ABCD.
text: This point X will be equidistant from all the four planes of the tetrahedron ABCD.
text: Let us consider a tetrahedron ABCD, having a mid sphere tangential to all the six edges.
text: Consider two triangles ADB and ADC, with AD as the common edge, and Φbc as the dihedral angle between them, which can fully describe the tetrahedron ABCD.
text: The center I of the sphere inscribed in a tetrahedron (ABCD) verifies I =