IUPAC name for 1,2,3-trichlorocyclopropane?
Achiral cyclic compounds like 1,2,3-trichlorocyclopropane may contain pseudoasymmetric centers.
Pseudoasymmetric centers have distinguishable ligands (“a”, “b”, “c”, “d”), two of which are nonsuperposable mirror images of each other (enantiomorphic). The lower case stereodescriptors “r” and “s” are used to designate the absolute configuration of pseudoasymmetric centers, for example (2⁠R,3⁠r,4⁠S)‑2,3,4‑trichloropentane:

Note that the stereodescriptors “r” and “s” describing a pseudoasymmetric stereogenic unit are invariant on reflection in a mirror (for example “r” remains “r”, and “s” remains “s”), but are reversed by the exchange of any two ligands (“r” becomes “s”, and “s” becomes “r”).
The configurations (“r” or “s”) at pseudoasymmetric stereogenic units are determined by application of the Cahn-Ingold-Prelog (CIP) priority system and the sequence rules. In particular, note that an atom or group with descriptor “R” has priority over its enantiomorph “S”. In order to establish the order of precedence of ligands in a stereogenic unit, the atoms of the stereogenic unit are rearranged in a hierarchical diagram, called a “digraph”. Descriptors specified in digraphs may correspond to the final descriptors or to temporary auxiliary descriptors used only for ranking ligands and never appearing as final descriptors.
Similar to the above-mentioned case of (2⁠R,3⁠r,4⁠S)‑2,3,4‑trichloropentane, the structure of (1⁠r)‑1,2,3‑trichlorocyclopropane contains one pseudoasymmetric center, which has two ligands that are nonsuperposable mirror images of each other:

The other isomer of 1,2,3‑trichlorocyclopropane is (1⁠s,2⁠s,3s)‑1,2,3‑trichlorocyclopropane, which contains three pseudoasymmetric centers. Each one has two ligands that are nonsuperposable mirror images of each other:


It may not be obvious how to choose the stereodescriptors ‘r’ or ‘s’ for 1,2,3-trisubstituted cyclopropanes. The ranking is a complex process and requires the use of auxiliary descriptors.
Generally, the stereodescriptors ‘r’ and ‘s’ are assigned by applying the Cahn-Ingold-Prelog (CIP) Priority System as for the stereodescriptors ‘R’ and ‘S’. The order of precedence is reached by the construction of a hierarchical digraph and the application of the Sequence Rules.
The constitutional formula of a cyclic molecule is transformed into an acyclic digraph according to the methodology that is described in Subsection P-92.1.4.3 of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) and which has been recommended by Prelog and Helmchen.
In order to obtain the acyclic digraph of a stereogenic unit, the didentate ligand (i.e. the ring) is transformed into two monodentate ligands by leaving intact in each case one bond with the core of the stereogenic unit and cleaving the other bond. At the end of each of the two branches thus obtained, a duplicate atom of the core is attached. (Note that this methodology is similar to the case of multiple bonds.) For example, for the pseudoasymmetric stereogenic unit at the atom numbered ‘1’ of (1​r)‑1,2,3‑trichlorocyclopropane:

where $\ce{(C)}$ is a duplicate representation of the core of the pseudoasymmetric stereogenic unit.
As the digraph is acyclic, it is now possible to specify the stereodescriptor ‘R’ or ‘S’ for the stereogenic unit at the atoms numbered ‘2’ and ‘3’ in each branch. These are auxiliary descriptors that are different in each branch.

Since the auxiliary descriptors are different, they allow the branches to be ranked using Sequence Rule 5, which states that ‘R’ has priority over ‘S’.

P-92.1.3.5 Sequence Rule 5


An atom or group with descriptor ‘R’, ‘M’, and ‘seqCis’ has priority over its enantiomorph ‘S’, ‘P’ or ‘seq Trans’.

Therefore, the configuration of the pseudoasymmetric stereogenic unit at the atom numbered ‘1’ of (1​r)‑1,2,3‑trichlorocyclopropane can be determined to be ‘r’.

In the same way, the configuration of each pseudoasymmetric stereogenic unit of (1⁠s,2⁠s,3⁠s)‑1,2,3‑trichlorocyclopropane can be determined as ‘s’.