A tetrahedron ABCD is isosceles if AB=BD, AC=BD, and AD=BC. In other words, in an isosceles tetrahedron the opposite edges are equal.
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tetrahedron
Only if it is a regular tetrahedron, regular octahedron, or regular icosahedron. All other geodesics have isosceles triangle faces, not equilateral triangles.
A triangular pyramid is usually called a tetrahedron; its base is an equilateral triangle, as are the other three of its sides. An Egyptian pyramid has a square base; the other four sides are isosceles triangles.
Well, a tetrahedron has four sides. A regular tetrahedron is a triangular pyramid.
A tetrahedron must be plane faced and so, it is just an ordinary tetrahedron.