This is an Aftermarket Starter Solenoid, by Rotary Corp. Part # 10772 is a 4 12v Pole Solenoid Starter with a max Torque setting of 35 lbs on the large Nuts, and 15 LBS on the small nuts. This is an Aftermarket Replacement for the following part numbers:

Ariens: 035510, 03551000, 045071, 04507100, 35510, 45071, AR03551000, AR04507100,
AYP: 103R, 109081X, 109946, 109946X, 110167, 138406X, 146154, 178661, 2008J, 21261, 24285, 3367R, 44429, 677A880, 7754R,
Bolens: 1752137, 1753539,
B&S 745001MA,
Brill: CG148736110,
Case: C-266525, C-33025, C33025,
Castelgarden: 118399062/0, 18736100/0, 1873611, 18736110/0, 18736111/0,
CCD: 725-04439A,
T-EXM: 1-513075, 110116, 1101162, 110167, 117-1197, 28-4210, 47-1910, 740207, 92-9845, TR28-4210, TR47-1910, 1-513075, 117-1197, 513075,
Gilson: 212655,
Grasshopper: 184251,
Gravely: 044766, 045071, 045071000, 45071,
Honda: CG18736100HO, CG18736110HO, CG18736111HO,
HOP: 532109081, 532109946, 532138406, 532146154, 532192507,
Ibea: 5080008, IP5080008,
JDi: AM130365, AM132990, AM133094, AM138497, GY00185,
Karsit: 000821117, 821117, MEJ-28,
Lawn-Boy: 740207,
Maestro: BAILEY 160-15, BAILEY 16015,
MTD: 725-04439A,
Ransomes: 1530,
Sabo: SB18736110,
Scag: 483278,
Simplicity: 1671993, 1685290, 1685290SM, 1686981, 1686981SM, 1686982, 1686982SM, 170051, 170051SM, 1700751, 1700751SM, 1722739,
Snapper: 1-8604, 1722739, 1755382YP, 18604, 7018604, 7075622, 7075622SM, 75622,
Stiga: 1134-2946-02, 1134-2962-01, 1134294602, 1134296201, 9400-0070-00, 94285, ST1134-2946-02, ST1134-2962-01,
Troy-Bilt: 1752137, 1752137P, 1753539,

Will accommodate Both 5/16" and 1/4" connectors
Mounting Bracket will accommodate Both Chassis and wall mount configurations.