To achieve secure communications, the cousins cryptography and steganography are used. The former scrambles secret messages in such way that only the intended recipient is capable of unscrambling them. The latter seeks to hide a secret message inside an innocuous message, audio, image, or video file (called the cover medium), in such a way that eavesdroppers will not suspect the very existence of the secret message. Combined, cryptography and steganography provide a secure form of communication: The former will encode the secret message in such a way that even if it intercepted, it is hard decrypt it; the latter will hide the encoded secret message. Images are the most popular cover medium used in steganography. Many different image file formats exist, most of them for specific applications. There are different steganographic algorithms for different image formats In this work, using the idea of splitting the cover image into several bit planes, I propose to hide secret messages in the intersection points of those planes with certain geometric objects. The resulting image containing the message is called stego-image. The latter should be such that a third party intercepting it will not have any indication that a secret message is present in the image. The geometric objects I have used are the cone and the hexagonal prism, and our technique has been implemented in both Matlab and Google Android.