Assertion: octahedron's face | /r/HasAspect | a line segment
Facets:
Source sentences:
text: D 2 d , [2 + ,4], (2*2): if one face has a line segment dividing the face into two equal rectangles, and the opposite has the same in perpendicular direction, the cube has 8 isometries; there is a symmetry plane and 2-fold rotational symmetry with an axis at an angle of 45° to that plane, and, as a result, there is also another symmetry plane perpendicular to the first, and another axis of 2-fold rotational symmetry perpendicular to the first.
text: , , (2*2): if one face has a line segment dividing the face into two equal rectangles, and the opposite has the same in perpendicular direction, the cube has 8 isometries; there is a symmetry plane and 2-fold rotational symmetry with an axis at an angle of 45° to that plane, and, as a result, there is also another symmetry plane perpendicular to the first, and another axis of 2-fold rotational symmetry perpendicular to the first.
text: : if each face has a line segment dividing the face into two equal rectangles, such that the line segments of adjacent faces do not meet at the edge, the cube has 24 isometries: the even permutations of the body diagonals and the same combined with inversion ( x is mapped to − x ).
text: , , (3*2): if each face has a line segment dividing the face into two equal rectangles, such that the line segments of adjacent faces do meet at the edge, the cube has 24 isometries: the even permutations of the body diagonals and the same combined with inversion ( is mapped to − ).