1. Usual Idol
The science behind the idol of Deity Ganesh is given in the ‘Shriganapatyatharvashirsha’ as ‘Ekadantam, Chaturhastam ….(एकदन्तं चतुर्हस्तं०)’, meaning one who has only one tooth (ekadanta), four hands (chaturbhuj), adorns a noose (pash) and a goad (ankush), holds a (broken) tooth in one hand and holds the other hand in a posture bestowing blessings (varadmudra), whose flag bears the symbol of a mouse, who has a red complexion, a large abdomen (lambodar), whose ears are like sifting pans, who adorns red clothes, whose body is smeared with a paste of red sandalwood (raktachandan) and who is worshipped with red flowers.
2. Some Variations
1. Mudra : Sometimes one comes across Ganapati idols in the lotus posture (padmasan) or at times even in the dancing posture (nrutyamudra).
2. Mundkata Ganesh : There is a beheaded (Mundkata) Ganesh idol in the Himalaya. The name itself suggests that this idol is without a head. It is said that this is the idol of the son who was created by deity Parvati from the coating of sebum on Her body and who was later beheaded by Deity Shankar.
3. Other complexions : Haridraganapati and the Urdhvaganapati have a yellow complexion. The Pingalganapati is tawny (pingat) while the Lakshmiganapati is white in complexion.
4. Linga : Just like Deity Shiva, Linga of Ganapati too exists. It is called Ganpatyalinga. It is shaped like a pomegranate, lemon, white gourd or jamun.
5. Nude : In the Tantra path of worship, the Ganesh idol is mostly nude. The Energy (Shakti) of Ganesh too accompanies the idol.
6. Feminine form : ‘In the Shakta sect, Deity Ganesh is worshipped in the feminine form. Some such examples are given below.
A. Ganeshvari : An extremely attractive sculpted idol of Ganeshvari is found in the Suchindram temple in Tamilnadu.
B. Ardha Ganeshvari : It has a highly meaningful form in the Tantra path of spiritual practice.
C. Ganeshani : This female deity is found in an extremely rare form of worship performed by tantriks and mantriks (followers of the Path of Tantra and Mantra).’
7. Types of Ganapati idols : There are several types of Ganapati idols like the Saumyaganapati, Balganapati, Herambganapati, Lakshmiganapati, Haridraganapati, Uchchishtaganapati, Suryaganapati, Varadganapati, Dvibhujganapati, Dashbhujganapati, Nartanganapati, Uttishthitganapati, Ganapati with the trunk curved towards the right, etc.
Reference: Sanatan Sanstha’s Holy text ‘Ganapati’