Tool insert and/or tool holder insert (74a-b, 78a-b), in particular tool storage insert and/or tool holder storage insert, having at least one base body (10a-b) comprising precisely one receiving region (14a-b), embodied at least partially as a hollow (12a-b) in the base body (10a-b), for at least partial accommodation of at least one tool and/or at least one tool holder (16a-b), having at least one contact element (18a-b, 20a-b, 22a-b), which is arranged at least partially in the receiving region (14a-b) and projects into the receiving region (14a-b), for the purpose of forming a contacting mounting of the tool and/or of the tool holder (16a-b), and having on at least two opposite-situated outer faces of the base body (10a-b) side walls (26a-b, 28a-b) which are realized so as to complement each other and extend parallel to a receiving direction (24a-b) of the receiving region (14a-b), the side walls (26a-b, 28a-b) comprising side surfaces (30a-b, 32a-b) which form contact faces, characterised in that the side surfaces (30a-b, 32a-b) of one side wall (26a-b) of the complementarily-realized side walls (26a-b, 28a-b), which form the contact faces, extend on at least two substantially different planes extending at least substantially parallel to each other, the side walls (26a-b) with the side surfaces (30a-b, 32a-b) which form the contact faces being configured to at least partially engage with side walls (26a-b, 28a-b) of further ones of the tool inserts and/or tool holder inserts (74a-b, 78a-b), also having side surfaces (30a-b, 32a-b) which form the contact faces, in such a way that - when the side walls (26a-b, 28a-b) of two of the tool inserts and/or tool holder inserts (74a-b, 78a-b) engage - imaginary smallest possible geometric cuboids, which in each case just still completely enclose one tool insert and/or tool holder insert (74a-b, 78a-b) of the two tool inserts and/or tool holder inserts (74a-b, 78a-b), at least partially overlap, the receiving region (14a-b) having precisely one receiving opening (66a-b), wherein a centre (104a-b) of the receiving opening (66a-b) and/or of the receiving region (14a-b) is arranged in the base body (10a-b) in a sidewise offset, and the tool insert and/or tool holder insert (74a-b, 78a-b) being shaped in such a way that - when tool inserts and/or tool holder inserts (74a-b, 78a-b) are lined up, which are in each case rotated by 180° in a horizontal plane - the receiving openings (66a-b) of the lined-up tool inserts and/or tool holder inserts (74a-b, 78a-b) are situated on two overlap-free parallel straight lines in rows (98a-b, 100a-b) which are offset from each other. having at least one base body (10a-b) comprising precisely one receiving region (14a-b), embodied at least partially as a hollow (12a-b) in the base body (10a-b), for at least partial accommodation of at least one tool and/or at least one tool holder (16a-b), having at least one contact element (18a-b, 20a-b, 22a-b), which is arranged at least partially in the receiving region (14a-b) and projects into the receiving region (14a-b), for the purpose of forming a contacting mounting of the tool and/or of the tool holder (16a-b), and having on at least two opposite-situated outer faces of the base body (10a-b) side walls (26a-b, 28a-b) which are realized so as to complement each other and extend parallel to a receiving direction (24a-b) of the receiving region (14a-b), the side walls (26a-b, 28a-b) comprising side surfaces (30a-b, 32a-b) which form contact faces, characterised in that the side surfaces (30a-b, 32a-b) of one side wall (26a-b) of the complementarily-realized side walls (26a-b, 28a-b), which form the contact faces, extend on at least two substantially different planes extending at least substantially parallel to each other, the side walls (26a-b) with the side surfaces (30a-b, 32a-b) which form the contact faces being configured to at least partially engage with side walls (26a-b, 28a-b) of further ones of the tool inserts and/or tool holder inserts (74a-b, 78a-b), also having side surfaces (30a-b, 32a-b) which form the contact faces, in such a way that - when the side walls (26a-b, 28a-b) of two of the tool inserts and/or tool holder inserts (74a-b, 78a-b) engage - imaginary smallest possible geometric cuboids, which in each case just still completely enclose one tool insert and/or tool holder insert (74a-b, 78a-b) of the two tool inserts and/or tool holder inserts (74a-b, 78a-b), at least partially overlap, the receiving region (14a-b) having precisely one receiving opening (66a-b), wherein a centre (104a-b) of the receiving opening (66a-b) and/or of the receiving region (14a-b) is arranged in the base body (10a-b) in a sidewise offset, and the tool insert and/or tool holder insert (74a-b, 78a-b) being shaped in such a way that - when tool inserts and/or tool holder inserts (74a-b, 78a-b) are lined up, which are in each case rotated by 180° in a horizontal plane - the receiving openings (66a-b) of the lined-up tool inserts and/or tool holder inserts (74a-b, 78a-b) are situated on two overlap-free parallel straight lines in rows (98a-b, 100a-b) which are offset from each other.