Are there any scriptural references of the trinity "Brahma, Vishnu, Mahesh(Shiva)" as depicted in popular culture?

Question

• Brahma is typically depicted as an ancient deity with multiple heads [& hands] in various directions.

• Vishnu is depicted in form of a deity sleeping in the midst of an ocean over a big snake (Shesha nAga) or sometimes as a person spread in the universe.

• Maheshwara (Shiva) is depicted in form of "Shiva Linga", where a male penis penetrates a female vagina

Are there any accurate or approximate scriptural references for displaying these trinity the way they are, in the popular culture?
Partial answers are also welcome.

Answer 1

Yes, we have scriptual refrences for the representation of Trinities:

Lord Brahma:

Scriptual refrences are avaliable in this answer

Seeing Brahma in such a condition, Satarupa went to heaven with the Manas sons of the Creator, and as she was travelling towards heaven, Brahma put on a fifth head right on top which afterwards He covered with His long matted hair. This is how Brahma came to have five heads. After this, Brahma lost his powers that He had acquired by practising acesticism, owing to His not controlling His mind and falling into the snares of Cupid. Then Brahma dispersed His sons, after directing them to carry on the work of Creation.

Lord Vishnu:

There are many many refrences. For eg. This chapter of Vishnu Purana:

The creator, Hari, sleeps upon the ocean, in the form of Brahmá--glorified by Sanaka And the saints who had gone to the Janaloka, and contemplated by the holy inhabitants of Brahmaloka, anxious for final liberation--involved in mystic slumber, the celestial personification of his own illusions, and meditating on his own ineffable spirit, which is called Vásudeva. This, Maitreya, is the dissolution termed incidental, because Hari, in the form of Brahmá, sleeps there, as its incidental cause. When the universal spirit wakes, the world revives; when he closes his eyes, all things fall upon the bed of mystic slumber. In like manner as a thousand great ages constitute a day of Brahmá, so his night consists of the same period; during which the world is submerged by a vast ocean. Awaking at the end of his night, the unborn, Vishńu, in the character of Brahmá, creates the universe anew, in the manner formerly related to you.

Lord Maheswara:

I discuss scriptual refrences about Shiva Linga in my answer here.

विशोध्य स्थापत्येद्भक्त्या सवेदिकमनुत्तमम् ।
लिंगवेदी उमा देवी लिंगं साक्षान् महेश्वर ।।

The Devotee shall clean Linga along with the pedestal and then devoutly install it. The pedestal of the Linga is Godess Uma and the Linga is Maheswara himself.

रुपित्वात्सकलस्तद्वत्तस्मात्सकलनिष्कल ।
निष्कलत्त्वान्निराकारं लिंगं तस्य समागतम् ।।

He is also Sakala as he has an embodied form. He is both Sakala and Niskala (formless/Nirguna). It is in his Niskala aspect that the Linga is appropriate as it represents formless aspect.

दहत्यूर्ध्वं स्थितो यच्म प्राणेत्पतिस्थितश्चयत् ।
स्थितलिङ्गस्य पन्नित्यं तस्मात्स्थाणुरिति स्मृतः ।।

Since he is great and ancient and is the source of the life and it's continuence and since his Linga form is everlasting, he is for that reason called Sthanu.

Thus we have plenty of refrences for representation of Trinities.

Answer 2

In Gita, I could find few relative references. I personally believe that "BrahmA", "Vishnu", "Shiva" all are the name of the same supreme reality, which is in oneness.

BrahmA

BG 13.14 - That (Knowable), which has hands and feet everywhere, which has eyes, heads and mouths everywhere, which has ears everywhere, exists in creatures by pervading them all.
BG 11.15 - ... Brahma the ruler, sitting on a lotus seat,
BG 5.10 - One who acts by dedicating actions to Brahman and by renouncing attachment, he does not become polluted by sin, just as a lotus leaf is not by water.

Hence, it's typically depicted with several heads, hands, legs, eyes & sitting on lotus unaffected from the Prakruti.

Vishnu

There is a namesake Vishnu reference, which refers to the sons of Aditi:

BG 10.21 - Among the Adityas [viz Dhata, Mitra, Aryama, Rudra, Varuna, Surya, Bhaga, Vivasvan, Pusa, Savita, Tvasta and Visnu.-Tr.] I am Vishnu; ... -- translation Gambhirananda

Few verses in chapter-11 depicts the famous all deity form:

BG 11.10 - Having many faces and eyes, possessing many wonderful sights, adorned with numerous celestial ornaments, holding many uplifted heavenly weapons;
BG 11.15 - Arjuna said O God, I see in Your body all the gods as also hosts of (various) classes of beings; Brahma the ruler, sitting on a lotus seat, and all the heavenly sages and serpents.
BG 11.16 - I see You as possessed of numerous arms, bellies, mouths and eyes; as having infinite forms all around. O Lord of the Universe, O Cosmic Person, I see not Your limit nor the middle, nor again the beginning!
BG 11.17 - I see You as wearing a diadem, wielding a mace, and holding a disc; a mass of brilliance glowing all around, difficult to look at from all sides, possessed of the radiance of the blazing fire and sun, and immeasurable.
BG 11.22 Those who are the Rudras, the Adityas, the Vasus and the Sadhyas, the Visve (-devas), the two Asvins, the Maruts and the Usmapas, and hosts of Gandharvas, Yaksas, demons and Siddhas-all of those very ones gaze at You, being indeed struck with wonder.
BG 11.23 - O mighty-armed One, seeing Your immense form with many mouths and eyes, having numerous arms, thighs and feet, with many bellies, and fearful with many teeth, the creatures are struck with terror, and so am I.

Another famous depiction of Vishnu is sleeping on Adi Shesha is discussed here.

Another form depicts as of whole universe silently pervades as the Vishnu:

BG 9.4 - This whole universe is pervaded by Me in My unmanifested form. All beings exist in Me, but I am not contained in them!

Shiva

"Shankara" is directly referred in Gita. Some people [mistakenly] consider "Shiva = Shankara":

BG 10.23 - Among the Rudras [Aja, Ekapada, Ahirbudhnya, Pinaki, Aparajita, Tryam-baka, Mahesvara, Vrsakapi, Sambhu, Harana and Isvara] I am Shankara, ... -- translation Gambhirananda

However, this is not the Rudra Shankara. But Shiva, which is the nirguna Brahman. Usually Shiva is depicted in the form of linga.
The linga (phallus) plants the seeds as a father and the yoni (womb), which accepts them as a mother to form the universe.

BG 14.3 - My womb is the great-sustainer. In that I place the seed. From that, O scion of the Bharata dynasty, occurs the birth of all things.
BG 14.4 - O son of Kunti, whatever forms are born from all the wombs, of them the great-sustainer is the womb; I am the father who deposits the seed.