According to the Siddhartha-samhita there are twenty-four forms of Lord Visnu, and these forms are named according to the position of the symbols in Their four hands

Expressions researched:
"and these forms are named according to the position of the symbolic representations in Their four hands" |"four hands" |"four-handed" |"twenty-four forms of Lord Visnu" |"twenty-four forms of Visnu"

SB Canto 3

There are twenty-four forms of Viṣṇu, each differently named.

SB 3.26.28, Purport:

The system of yoga entails controlling the mind, and the Lord of the mind is Aniruddha. It is stated that Aniruddha is four-handed, with Sudarśana cakra, conchshell, club and lotus flower. There are twenty-four forms of Viṣṇu, each differently named. Among these twenty-four forms, Saṅkarṣaṇa, Aniruddha, Pradyumna and Vāsudeva are depicted very nicely in the Caitanya-caritāmṛta, where it is stated that Aniruddha is worshiped by the yogīs. Meditation upon voidness is a modern invention of the fertile brain of some speculator. Actually the process of yoga meditation, as prescribed in this verse, should be fixed upon the form of Aniruddha. By meditating on Aniruddha one can become free from the agitation of acceptance and rejection. When one's mind is fixed upon Aniruddha, one gradually becomes God-realized; he approaches the pure status of Kṛṣṇa consciousness, which is the ultimate goal of yoga.

CC Madhya-lila

There are twenty-four forms of Lord Viṣṇu.

CC Madhya 20.223, Purport:

“According to the Siddhārtha-saṁhitā there are twenty-four forms of Lord Viṣṇu. First I shall describe, according to the opinion of that book, the location of the weapons, beginning with the disc."

The twenty-four forms are:

(1) Vāsudeva;

(2) Saṅkarṣaṇa;

(3) Pradyumna;

(4) Aniruddha;

(5) Keśava;

(6) Nārāyaṇa;

(7) Mādhava;

(8) Govinda;

(9) Viṣṇu;

(10) Madhusūdana;

(11) Trivikrama;

(12) Vāmana;

(13) Śrīdhara;

(14) Hṛṣīkeśa;

(15) Padmanābha;

(16) Dāmodara;

(17) Puruṣottama;

(18) Acyuta;

(19) Nṛsiṁha;

(20) Janārdana;

(21) Hari;

(22) Kṛṣṇa;

(23) Adhokṣaja and;

(24) Upendra.

Teachings of Lord Caitanya

The twenty-four forms of Viṣṇu are named according to the position of the symbolic representations in Their four hands.

Teachings of Lord Caitanya, Chapter 7:

The different forms of Kṛṣṇa are distributed throughout the universe to give pleasure to the devotees. It is not that devotees are born only in India. There are devotees in all parts of the world, but they have simply forgotten their identity. These forms incarnate not only to give pleasure to the devotee but to reestablish devotional service and perform other activities which vitally concern the Supreme Personality of Godhead. Some of these forms are incarnations mentioned in the scriptures, such as the Viṣṇu incarnation, Trivikrama incarnation, Nṛsiṁha incarnation and Vāmana incarnation.

In the Siddhārtha-saṁhitā, there is a description of the twenty-four forms of Viṣṇu, and these forms are named according to the position of the symbolic representations in Their four hands. When one describes the positions of objects in the hands of the Viṣṇu mūrti, one should begin with the lower right hand then move to the upper right hand, upper left hand and, finally, to the lower left hand. In this way,

Vāsudeva may be described as being represented by mace, conch shell, disc and lotus flower;

Saṅkarṣaṇa is represented by mace, conch shell, lotus flower and disc. Similarly;

Pradyumna is represented by disc, conch shell, mace and lotus flower;

Aniruddha is represented by disc, mace, conch shell and lotus flower.

In the spiritual sky the representations of Nārāyaṇa are twenty in number and are described as follows:

Śrī Keśava (flower, conch shell, disc, mace);

Nārāyaṇa (conch, flower, mace and disc);

Śrī Mādhava (mace, disc, conch and flower);

Śrī Govinda (disc, mace, flower and conch);

Viṣṇu-mūrti (mace, flower, conch and disc);

Madhusūdana (disc, conch, flower and mace);

Trivikrama (flower, mace, disc and shell);

Śrī Vāmana (conch, disc, mace and flower);

Śrīdhara (flower, disc, mace and shell);

Hṛṣīkeśa (mace, disc, flower and conch);

Padmanābha (shell, flower, disc and mace);

Dāmodara (flower, disc, mace and shell);

Puruṣottama (disc, flower, shell and mace);

Acyuta (mace, flower, disc and shell);

Nṛsiṁha (disc, flower, mace and shell);

Janārdana (flower, disc, shell and mace);

Śrī Hari (shell, disc, flower and mace);

Śrī Kṛṣṇa (shell, mace, flower and disc);

Adhokṣaja (flower, mace, shell and disc), and;

Upendra (shell, mace, disc and flower).

Srimad-Bhagavatam Lectures

There are twenty-four forms of Viṣṇu, śaṇkha-cakra-gadā-padma, according to Their placing in different hands.

Lecture on SB 6.1.33 -- San Francisco, July 18, 1975:

In the Vaikuṇṭha they also keep themselves four-handed as Viṣṇu, Nārāyaṇa. So the Vaiṣṇavas are very intelligent. They want to keep themself in as good as God. Sometimes more than God, Vaiṣṇava. That is very intelligent. What is the use of becoming one? I lose my individuality. So that is jñānī's aspiration. But the bhaktas, they want to keep association with Kṛṣṇa or Viṣṇu in the same opulence, same prosperity, everything, bodily features the same, everything.

So advaitam acyutam anādim ananta-rūpam ādyaṁ purāṇa-puruṣaṁ nava-yauvanaṁ ca (Bs. 5.33). So nava-yauvanam. Lord Viṣṇu, Nārāyaṇa, Kṛṣṇa, or the liberated devotees there, they are of the same bodily feature, nava-yauvanam, always young. Therefore it is said, sarve ca nūtna-vayasaḥ. Vayasaḥ means age, and nūtna means just fresh young man. Nūtna-vayasaḥ sarve cāru-caturbhujāḥ: "All of you are very beautiful, with four hands." So even the living entities they have got also four hands, not empty hands, with good ornament, good dress, and the complexion, color—everything like Viṣṇu. Everything like Viṣṇu. Sarve cāru-caturbhujāḥ, dhanur-niṣaṅgāsi-gadā-śaṇkha-cakrāmbuja-śriyaḥ. And the weapons: dhanuḥ, bow; dhanur-niṣaṅga asi, the arrows and the sword; gadā, club; śaṇkha, conchshell; and cakra, disc. As Viṣṇu has Sudarśana... Śaṅkha-cakra-gadā-padma. There are fourteen different forms of Viṣṇu according to the position of the weapon in different hand, beginning with śaṇkha-cakra-gadā-padma, then cakra-gadā-śaṇkha-padma, in this way. These description are there in the Caitanya-caritāmṛta. And according to the change of the weapon, the different names are there. One viṣṇu-mūrti is called Vāmana; one mūrti is called Govinda. In this way there are twenty-four forms of Viṣṇu, śaṇkha-cakra-gadā-padma, according to Their placing in different hands.