It is not an exaggeration if we say that the form of Lord Nr̥siṁha and Varāha are more interesting than any other emanations of Srīmannārāyaṇa. Their Vigrahas are also equally fascinating.
Generally, the mūrti of Varāha is described as human up to the neck and the face is of Varāha or boar (Pādma Samhitā). The hue of this mūrti has been variously described as white (like the conch), śyāma, blue, green or black, when sources such as Nāradīya, Parāśara, Pādma and Sātvata Samhitās are examined. The hands of this mūrti range from four (Hayaśīrṣa Samhitā) to sixteen (Parāśara Samhitā). According to Nāradīya Samhitā, the mūrti of Varāha is to be thus constructed:
‘The right and left hands on the back hold the Chakra and the Shankha; With the front two hands, he holds Bhūdēvī (earth personified), seating her on his left lap, with his snout affectionately smelling the fragrance of the goddess, holding her two feet with his right hands, embracing her lovingly with his left hand. The mūrti is decorated with a crown and various ornaments and is seated on a pedestal. One of his feet remains raised. The idol should always be seated (āsīna) and not reclining etc. (śayāna, yānaga).
Vimānārcana Kalpa, which belongs to the Vaikhānasāgama, lists three forms of Varāha mūrtis that can be consecrated:
1 ādivarāha
2 Pralayavarāha
3 Yajñavarāha
If there is one mūrti that is described in almost every āgama of Pāñcarātra and Vaikhānasa streams, that would be of Nr̥simha. The mūrti of Nr̥simha can be sthita, āsīna or yānaga. Of these, the popular is the āsīna or seated form, popularly called Yogāsana mūrti. In the first two forms, the body is of a man and the face that of a Lion. He has three eyes, and a fearful face sporting daṁṣṭra. According to Viṣvaksēna Samhitā and Viṣṇu Tantra, the idol should have two hands sporting Shankha and Chakra. However, most other samhitās illustrate four hands holding Shankha, Chakra, Gadā and Padma. Hayaśīrṣa samhitā describes a similar form, where padma is replaced by abhaya mudrā. It also illustrates a second form where the upper two hands hold Shankha and Chakra, while the bottom two hands are engaged in ripping open the innards of an asura on the Lord’s lap.
The aṣṭabhuja and ṣōḍaśabhuja forms of Nr̥simha are also variously described. The procedure is to install Brahmā to the right and Rudra to the left, as parivāra. Prahlāda and Garuḍa are also present in the vicinity.
In most temples which have Nr̥simha as the central deity, the commonly suggested form is of Saumya Chaturbhuja mūrti along with śrī and Bhūdēvīs. Pādma samhitā describes forms with and without Bhūdēvī. Consecration of the Lord in reclining form is prohibited by various āgamas. General non-specific lakṣaṇas of sthānaga and yānaga mūrtis are similar that of Vāsudēva mūrti.
There is a reference to Puccha Nr̥simha mūrti in īśvara samhitā, where the tail of the mūrti is engaged in tāḍana of the earth, thereby bringing Pralaya.
Vihagendra Samhitā lists seventy-four forms: svayam nr̥simha, mōkṣanr̥simha, vijayanr̥simha, chatranr̥simha, dīrghanr̥simha, virūpanr̥simha, pūrṇanr̥simha, abdhinr̥simha, lakṣmīnr̥simha, vijayalakṣmī nr̥simha, yōganr̥simha, yōgēśvaranr̥simha, dīptinr̥simha, puṣṭinr̥simha, bhūtaprabhāthi nr̥simha, jvālānr̥simha, ugranr̥simha, ghōranr̥simha, vidāraṇanr̥simha, ahōbala nr̥simha, stambhanr̥simha, mahānr̥simha, pātāla nr̥simha, ananta nr̥simha, grahaṇanr̥simha, pramathanr̥simha, āvēśa nr̥simha, aṭṭahāsa nr̥simha, navavyūha nr̥simha, cakranr̥simha, dik nr̥simha, caṇḍanr̥simha, aranr̥simha, prāsādanr̥simha, brahmanr̥simha, viṣṇunr̥simha, raudranr̥simha, mārtāṇḍa nr̥simha, candranr̥simha, bhairava nr̥simha, pr̥thivī nr̥simha, vāyunr̥simha, ākāśa nr̥simha, jvalana nr̥simha, ādhāra nr̥simha, amr̥ta nr̥simha, haṁsa nr̥simha, ātmanr̥simha, satyanr̥simha, yajñanr̥simha, annadāna nr̥simha, prabhāsa nr̥simha, viśvarūpa nr̥simha, tritāra nr̥simha.
The list names fifty-four forms, but if the numbers for vyūha, nava and dik are added, the count does become seventy-four.