why doesn't the circular representation for the 3-bar rotoinversion show the atoms below the plane as empty circles like with all the other rotoinversions?
That's an oversight on my part. The projection drawing at the top for the 3-fold rotoinversion axis should have three filled circles and three empty circles.
At 5:23, I did not understand as after 4 operation, why it is negative y-axis as we are at the same point where we were earlier when we rotate about the z-axis and also why have you changed the positioning of x y and z too?
In a 90° rotation, imagine the x-y plane. When you rotate counterclockwise, the x-coordinate moves to where the y-coordinate was, and the y-coordinate moves to the negative side of the x-axis. This explains the change from (x, y, z) to (-y, x, z).
Also at 7:10, why is that for every operation circle is getting changed. Like in first case, from dark to white. In 2nd case the dark circle is inside of white circle and in third case we have two white circle and two black. And also i think, you have explained wrong for 4bar case, as the rotation is of 90 degree and you have marked or explained incorrectly!! Do let me know your thoughts about this.
dark circle means above the plan. After the inversion through the point, they will fall below the XY plane. So we represent the below plan points as white circles.
why doesn't the circular representation for the 3-bar rotoinversion show the atoms below the plane as empty circles like with all the other rotoinversions?
That's an oversight on my part. The projection drawing at the top for the 3-fold rotoinversion axis should have three filled circles and three empty circles.
At 5:23, I did not understand as after 4 operation, why it is negative y-axis as we are at the same point where we were earlier when we rotate about the z-axis and also why have you changed the positioning of x y and z too?
In a 90° rotation, imagine the x-y plane. When you rotate counterclockwise, the x-coordinate moves to where the y-coordinate was, and the y-coordinate moves to the negative side of the x-axis. This explains the change from (x, y, z) to (-y, x, z).
Can you please share the pdf if possible ?
Also at 7:10, why is that for every operation circle is getting changed. Like in first case, from dark to white. In 2nd case the dark circle is inside of white circle and in third case we have two white circle and two black. And also i think, you have explained wrong for 4bar case, as the rotation is of 90 degree and you have marked or explained incorrectly!! Do let me know your thoughts about this.
dark circle means above the plan. After the inversion through the point, they will fall below the XY plane. So we represent the below plan points as white circles.