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Abstract Logos are logos where the product or service of that company is being represented through an abstract/artistic symbol or icon.
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Letterform Logos are logos that use the shape of a letter used in typography, calligraphy, paleography, and epigraphy to represent their company. This can also include numbers and punctuation.
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Pictorial Logos, also sometimes referred to as brand marks or a logo symbol, are icon—or graphic-based designs. This type of logo is probably the image that comes to mind when most people think “logo”.
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Wordmark Logos are the written name of the organization, company or product, stylized in a way that is meant to stand out in their customer’s mind.