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A tool assembly comprising a tool member receivable in a recess formed in a driven member. The tool member comprises a shank element, a plurality of tier elements integrally stacked coaxially thereon, and an apex element. Each of the tier and apex elements comprises first and second torque sections,

A tool assembly comprising a tool member receivable in a recess formed in a driven member. The tool member comprises a shank element, a plurality of tier elements integrally stacked coaxially thereon, and an apex element. Each of the tier and apex elements comprises first and second torque sections, each of which comprise first and second side surfaces subtending the same predetermined angle, a riser surface interconnecting the side surfaces, and a step surface. The recess in the driven member is characterized by member walls which are drivingly engagable with the side surfaces of the tool member.

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1. A tool for transmitting an externally applied torque to an object, comprising: a shank element, longitudinally rotatable about a tool axis, for receiving an externally applied torque; a first tier element, rotatable with and supported by the shank element and having invariant cross-section al

1. A tool for transmitting an externally applied torque to an object, comprising: a shank element, longitudinally rotatable about a tool axis, for receiving an externally applied torque; a first tier element, rotatable with and supported by the shank element and having invariant cross-section along the tool axis, comprising: a first torque section, comprising: first and second side surfaces, spaced from and extending radially inward in relation to the tool axis, the first and second side surfaces subtending a predetermined angle with respect to the tool axis; a riser surface extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces; and a step surface extending perpendicularly to the tool axis and inwardly from the riser surface, while remaining spaced from the tool axis; and a second torque section, comprising: first and second side surfaces, spaced from and extending radially inward in relation to the tool axis, the first and second side surfaces subtending the same predetermined angle, relative to the tool axis, as that subtended by the first and second side surfaces of the first torque section; a riser surface extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces; and a step surface extending perpendicularly to the tool axis and inwardly from the riser surface, while remaining spaced from the tool axis; and an apex element, supported at a position on the tool axis move distant from the shank element than the first tier element, rotatable with the shank element, and having an invariant cross-section along the tool axis, comprising: a first torque section, comprising: first and second side surfaces, extending radially inward in relation to the tool axis, the first and second side surfaces subtending the same predetermined angle, relative to the tool axis, as that subtended by the first and second side surfaces of the first torque section of the first tier element, with the first side surface coplanar with the first side surface of the first torque section of the first tier element, and with the second side surface coplanar with the second side surface of the first torque section of the first tier element; a riser surface, extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces, the riser surface having an average distance from the tool axis which is smaller than the average distance of the riser surface of the first tier element from the tool axis; and an apex surface extending perpendicularly to the tool axis and extending inwardly fron the riser surface, while remaining spaced from the tool axis; and a second torque section, comprising: first and second side surfaces, extending radially inward from in relation to the tool axis, the first and second side surfaces subtending the same predetermined angle, relative to the tool axis, as that subtended by the first and second side surfaces of the second torque sections of the first tier element, with the first side surface coplanar with the first side surface of the second torque section of the first tier element, and with the second side surface coplanar with the second side surface of the second torque section of the first tier element; a riser surface, extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces, the riser surface having an average distance from the tool axis which is smaller than the average distance of the riser surface of the first tier element from the tool axis; and an apex surface extending perpendicularly to the tool axis and extending inwardly from the riser surface, while remaining spaced from the tool axis. 2. The apparatus of claim 1 in which each riser surface of each torque section of each tier and apex element extends concentrically with respect to the tool axis. 3. The apparatus of claim 2 in which the first tier element further comprises: a core section concentric with the tool axis and integral with the first and second torque sections; and in which the apex element further comprises: a core section concentric with the tool axis and integral with the first and second torque sections. 4. The apparatus of claim 2 in which the first tier element is characterized as one of a plurality of tier elements, each tier element comprising: a first torque section having first and second side surfaces coplanar with the first and second side surfaces of the first torque section of the first tier element, a riser surface and a step surface; a second torque section having first and second side surfaces coplanar with the first and second side surfaces of the second torque section of the first tier element, a riser surface and a step surface; wherein each tier element supports the adjacent tier element more distant from the shank element, wherein the tier element most distant from the shank element supports the apex element, wherein the riser surface of each tier element is nearer to the tool axis than the riser surface of the adjacent tier element nearer the shank element, and wherein the riser surface of the apex element is nearer the tool axis than the riser surface of the adjacent tier element nearer the shank element. 5. A tool assembly for transmission of an externally applied torque, comprising: a tool member comprising: a shank element, longitudinally rotatable about a tool axis, for receiving an externally applied torque; a first tier element, rotatable with and supported by the shank element and having invariant cross-section along the tool axis, comprising: a first torque section, comprising: first and second side surfaces, spaced from and extending radially inward in relation to the tool axis, the first and second side surfaces subtending a predetermined angle with respect to the tool axis; a riser surface extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces; and a step surface extending perpendicularly to the tool axis and inwardly from the riser surface, while remaining spaced from the tool axis; and a second torque section, comprising: first and second side surfaces, spaced from and extending radially inward in relation to the tool axis, the first and second side surfaces subtending the same predetermined angle, relative to the tool axis, as that subtended by the first and second side surfaces of the first torque section; a riser surface extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces; and a step surface extending perpendicularly to the tool axis and inwardly from the riser surface, while remaining spaced from the tool axis; and an apex element, supported at a position on the tool axis more distant from the shank element than the first operating element, rotatable with the shank element, and having an invariant cross-section along the tool axis, comprising: a first torque section, comprising: first and second side surfaces, extending radially inward in relation to the tool axis, the first and second side surfaces subtending the same predetermined angle, relative to the tool axis, as that subtended by the first and second side surfaces of the first torque section of the first tier element, with the first side surface coplanar with the first side surface of the first torque section of the first tier element, and with the second side surface coplanar with the second side surface of the first torque section of the first tier element; a riser surface, extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces, the riser surface having an average distance from the tool axis which is smaller than the average distance of the riser surface of the first tier element from the tool axis; and an apex surface extending perpendicularly to the tool axis and extending inwardly from the riser surface, while remaining spaced from the tool axis; and a second torque section, comprising: first and second side surfaces, extending radially inward from in relation to the tool axis, the first and second side surfaces subtending the same predetermined angle, relative to the tool axis, as that subtended by the first and second side surfaces of the second torque sections of the first tier element, with the first side surface coplanar with the first side surface of the second torque section of the first tier element, and with the second side surface coplanar with the second side surface of the second torque section of the first tier element; a riser surface, extending longitudinally with respect to the tool axis, and extending laterally between the first and second side surfaces, the riser surface having an average distance from the tool axis which is smaller than the average distance of the riser surface of the first tier element from the tool axis; and an apex surface extending perpendicularly to the tool axis and extending inwardly from the riser surface, while remaining spaced from the tool axis; and a driven member rotatable about a member axis and having a plurality of member walls defining a recess, the tool member receivable therein, the recess characterized as having member walls drivingly engagable with each of the first and second side surfaces of the first and second torque sections of the apex element of the tool member. 6. The apparatus of claim 5 in which the recess of the driven member is further characterized as having a member wall engagable with the apex surfaces of the first and second torque sections of the apex element. 7. The apparatus of claim 5 in which the recess of the drive member is further characterized as having member walls drivingly engagable with the first and second side surfaces of the first and second torque sections of the first tier element. 8. The apparatus of claim 7 in which the recess of the driven member is further characterized as having a member wall engagable with the step surfaces of the first and second torque sections of the first tier element. 9. A drive assembly for transmission of an externally applied torque, comprising: a tool member, comprising: a shank element longitudinally rotatable about a tool axis, for receiving an externally applied torque; a plurality of tier elements having invariant cross-section along the tool axis, each tier element comprising: a first torque section comprising: first and second side surfaces extending radially with respect to the tool axis and spaced therefrom, the first and second side surfaces coplanar with the first and second side surfaces of the first torque section of each other tier element; a riser surface; and a step surface; and a second torque section comprising: first and second side surfaces extending radially with respect to the tool axis and spaced therefrom, the first and second side surfaces coplanar with the first and second side surfaces of the second torque section of each other tier element; a riser surface; and a step surface; wherein each tier element supports the adjacent tier element more distant from the shank element, and wherein the riser surface of each tier element is nearer to the tool axis than the riser surface of the adjacent tier element nearer the shank element; and a driven member, rotatable about a member axis and having a plurality of member walls defining a recess, the tool member receivable therein, the recess characterized as having member walls drivingly engagable with each of the first and second side surfaces of the first and second torque sections of a selected tier element. 10. The apparatus of claim 9 in which the recess of the driven member is further characterized as having member walls drivingly engagable with each of the first and second side surfaces of each of the first and second torque sections of each tier element located farther from the shank element than the selected operating element.