Assertion: tetrahedron's face | /r/HasProperty | congruent
Facets:
value: to each other
type: TRANSITIVE-OBJECT
value: in a triangular pyramid
type: LOCATION
value: tetragonal trapezohedron
type: LOCATION
Source sentences:
text: (This means no 4 faces are congruent.)
text: An isosceles tetrahedron, also called a disphenoid, is a tetrahedron where all four faces are congruent triangles.
text: Tetragonal trapezohedron: The eight faces are congruent kites.
text: But it is not exclusive because it applies to any tetrahedron having four congruent faces, even if they are scalene.
text: A regular tetrahedron is a special case of both the general tetrahedron and the isosceles tetrahedron for which all four triangular faces are not only congruent, but are also equilateral triangles, i.e. triangles for which all three sides are the same length, and all internal angles are sixty degrees (60°).
text: From this, it should be relatively easy to see that the four faces of the isosceles tetrahedron are congruent, since each of the four triangular faces is composed of one of the following combinations of sides:
text: If the tetrahedron is isosceles, life is somewhat simpler because the four faces will be congruent, and will therefore all have the same area.
text: A regular tetrahedron is a closed polyhedron with four equilateral triangular faces (all faces are congruent), where sets of 3 faces meet at a point.
text: Therefore no three faces can be congruent.
text: Even though all the faces are congruent, the rhombic icosahedron is not face-transitive.
text: In a Triangular Pyramid, the lateral faces are all congruent to each other, but not always with the base triangle.
text: The lateral faces need to be congruent if it is a right pyramid, not otherwise.
text: One more case here is isosceles tetrahedron where all four faces would be congruent triangles.
text: The faces of an isosceles tetrahedron are congruent triangles