An exact echo occurs when all the pieces in the two (or more) formations concerned are in the same positions relative to each other. Only the pattern formed by the pieces is echoed, other aspects are ignored.
Before I present some examples of such exactly echoed arrangement of pieces, I want to turn your attention to the following stunning chess problem which has echoed moves.
A. Benedek  
The Problemist 5/1977  
h#2  (3+10) 
a) Diagram b) Rotate 90° 
The solution is
a) 1. Kc5 Bb3 2. Bd4 Bxe7#
b) 1. Kc5 Bb3 2. Bd4 Bxe7#
Yes, though the position is rotated, the moves are absolutely identical. Fantastic!
Now, let's have a look at some exact echo problems in which the echoed configurations are related by a shift of one or two ranks.




Solutions
1a  *1.  Kf4 2. d3 Qf5+ 3. Kh6 Ne5 4. e3# 1. g3 Nd4 2. f3 Ne6 3. d4 Rg5 4. e4# 
1b  1. Qd6! 1.  e5 2. Qd7+ Kf6 3. Nf2 e4 4. Ng4# 1.  Kf6 2. Kh6 Kf7 3. Qd8 e5 4. Ng5# 
2a  1. Bf4 Nb4 2. Rd4 Kf1 3. Ke3 Ke1 4. Re4 Nc2# 1. Bf6 Nb2 2. Ke5 e4 3. Rd6 Ke3 4. Re6 Nc4# 
2b  1. Qf7! with the thematic lines 1.  Kh5 2. Kf4 Kh6 3. h4 g5+ 4. h×g5# 1.  g5 2. Kf2 g4 3. Qf5 g3+ 4. h×g3# 
If you bother to examine the different types of exact echoes, you'll find out that there are only five: identity, translation, rotation, reflection and glide reflection. I won't further elaborate on that, you'll surely find appropriate information yourself.
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