A bench headed by Chief Justice R M Lodha will hear the pleas in which the petitioners have submitted that the high court order to demolish the towers -- Apex and Ceyane - be immediately stayed.
Real estate developer Supertech has also filed a separate appeal against the high court's verdict.
The two towers have 857 apartments in total. Of these, about 600 flats have already been sold.
In the petition, the firm has claimed that the two towers were being constructed as per "approved building plans" and "there is no violation".
On April 11, the Allahabad HC had ordered demolition of the two towers and directed the company to refund money to the homebuyers.
The High Court order came on a petition of the Emerald Court Owner Resident Welfare Association, which had alleged that the approval and construction of the two towers was "in complete violation of the Uttar Pradesh Apartment (Promotion of Construction, Ownership and Maintenance) Act".
The petitioner also claimed the Noida authority had given permission to raise the height of the two towers, which was earlier supposed to have only 24 floors each, "without maintaining the mandatory distance of 16 metres from an adjoining building block, making it "unsafe, apart from blocking air and light".
RESULT
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by the Allahabad High Court order to demolish the company's two 40-storeyed towers in Noida. Supertech will move the Supreme Court next week
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