I  have found 120 algorithms for the Megaminx based on the Ih point group.

In turn, these 120 algorithms can represent the Ih point group.

For example, if B1W3B1A1B4W4B4W1B1A4B4W4B1W3B4 represents e,

then C1W3C1B1C4W4C4W1C1B4C4W4C1W3C4 represents W[5^1].

Therefore, there are 120 such algorithms in total.

The algorithm B1W3B1A1B4W4B4W1B1A4B4W4B1W3B4 = e;

The algorithm C1W3C1B1C4W4C4W1C1B4C4W4C1W3C4 = W[5^1];

The algorithm D1W3D1C1D4W4D4W1D1C4D4W4D1W3D4 = W[5^2];

The algorithm E1W3E1D1E4W4E4W1E1D4E4W4E1W3E4 = W[5^3];

The algorithm A1W3A1E1A4W4A4W1A1E4A4W4A1W3A4 = W[5^4];

The algorithm W1E3W1A1W4E4W4E1W1A4W4E4W1E3W4 = A[5^1];

The algorithm E1N2E1A1E4N1E4N4E1A4E4N1E1N2E4 = A[5^2];

The algorithm N4F2N4A1N1F1N1F4N4A4N1F1N4F2N1 = A[5^3];

The algorithm F4B3F4A1F1B4F1B1F4A4F1B4F4B3F1 = A[5^4];

The algorithm B1A3B1F4B4A4B4A1B1F1B4A4B1A3B4 = B[5^1];

The algorithm B1F2B1G4B4F1B4F4B1G1B4F1B1F2B4 = B[5^2];

The algorithm B1G2B1C1B4G1B4G4B1C4B4G1B1G2B4 = B[5^3];

The algorithm B1C3B1W1B4C4B4C1B1W4B4C4B1C3B4 = B[5^4];

The algorithm G4B3G4F4G1B4G1B1G4F1G1B4G4B3G1 = C[5^1];

The algorithm H4G2H4S4H1G1H1G4H4S1H1G1H4G2H1 = C[5^2];

The algorithm D1H2D1M4D4H1D4H4D1M1D4H1D1H2D4 = C[5^3];

The algorithm W1D3W1E1W4D4W4D1W1E4W4D4W1D3W4 = C[5^4];

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6C5:

Megaminx = Ih Point Group: (1): W[5^1]

Megaminx = Ih Point Group: (1): W[5^1](2nd edition) (youtube.com)

Megaminx = Ih Point Group: (2): A[5^1]

Megaminx = Ih Point Group: (2): A[5^1](2nd edition) (youtube.com)

Megaminx = Ih Point Group: (3): B[5^1]

Megaminx = Ih Point Group: (3): B[5^1](2nd edition) (youtube.com)

Megaminx = Ih Point Group: (4): C[5^1]

Megaminx = Ih Point Group: (4): C[5^1] (youtube.com)

Megaminx = Ih Point Group: (5): D[5^1]

Megaminx = Ih Point Group: (5): D[5^1] (youtube.com)

Megaminx = Ih Point Group: (6): E[5^1]

Megaminx = Ih Point Group: (6): E[5^1] (youtube.com)

6C5^2:

Megaminx = Ih Point Group: W[5^2](To be published)

Megaminx = Ih Point Group: A[5^2] (To be published)

Megaminx = Ih Point Group: B[5^2] (To be published)

Megaminx = Ih Point Group: C[5^2] (To be published)

Megaminx = Ih Point Group: D[5^2] (To be published)

Megaminx = Ih Point Group: E[5^2] (To be published)

6C5^3:

Megaminx = Ih Point Group: W[5^3] (To be published)

Megaminx = Ih Point Group: A[5^3] (To be published)

Megaminx = Ih Point Group: B[5^3] (To be published)

Megaminx = Ih Point Group: C[5^3] (To be published)

Megaminx = Ih Point Group: D[5^3] (To be published)

Megaminx = Ih Point Group: E[5^3] (To be published)

6C5^4:

Megaminx = Ih Point Group: W[5^4] (To be published)

Megaminx = Ih Point Group: A[5^4] (To be published)

Megaminx = Ih Point Group: B[5^4] (To be published)

Megaminx = Ih Point Group: C[5^4] (To be published)

Megaminx = Ih Point Group: D[5^4] (To be published)

Megaminx = Ih Point Group: E[5^4] (To be published)

10C3:

Megaminx = Ih Point Group: (7): WAB[3^1]

Megaminx = Ih Point Group: (7): WAB[3^1] (youtube.com)

Megaminx = Ih Point Group: (8): WBC[3^1]

Megaminx = Ih Point Group: (8): WBC[3^1] (youtube.com)

Megaminx = Ih Point Group: (9): WCD[3^1]

Megaminx = Ih Point Group: (9): WCD[3^1] (youtube.com)

Megaminx = Ih Point Group: (10): WDE[3^1]

Megaminx = Ih Point Group: (10): WDE[3^1] (youtube.com)

Megaminx = Ih Point Group: (11): WEA[3^1]

Megaminx = Ih Point Group: (11): WEA[3^1] (youtube.com)

Megaminx = Ih Point Group: (12): ABF[3^1]

Megaminx = Ih Point Group: (12): ABF[3^1] (youtube.com)

Megaminx = Ih Point Group: (13): BCG[3^1]

Megaminx = Ih Point Group: (13): BCG[3^1] (youtube.com)

Megaminx = Ih Point Group: (14): CDH[3^1]

Megaminx = Ih Point Group: (14): CDH[3^1] (youtube.com)

Megaminx = Ih Point Group: (15): DEM[3^1]

Megaminx = Ih Point Group: (15): DEM[3^1] (youtube.com)

Megaminx = Ih Point Group: (16): EAN[3^1]

Megaminx = Ih Point Group: (16): EAN[3^1] (youtube.com)

10C3^2:

Megaminx = Ih Point Group: WAB[3^2] (To be published)

Megaminx = Ih Point Group: WBC[3^2] (To be published)

Megaminx = Ih Point Group: WCD[3^2] (To be published)

Megaminx = Ih Point Group: WDE[3^2] (To be published)

Megaminx = Ih Point Group: WEA[3^2] (To be published)

Megaminx = Ih Point Group: ABF[3^2] (To be published)

Megaminx = Ih Point Group: BCG[3^2] (To be published)

Megaminx = Ih Point Group: CDH[3^2] (To be published)

Megaminx = Ih Point Group: DEM[3^2] (To be published)

Megaminx = Ih Point Group: EAN[3^2] (To be published)

15C2:

Megaminx = Ih Point Group: (17): WA[2]

Megaminx = Ih Point Group: (17): WA[2] (youtube.com)

Megaminx = Ih Point Group: (18): WB[2]

Megaminx = Ih Point Group: (18): WB[2] (youtube.com)

Megaminx = Ih Point Group: (19): WC[2]

Megaminx = Ih Point Group: (19): WC[2] (youtube.com)

Megaminx = Ih Point Group: (20): WD[2]

Megaminx = Ih Point Group: (20): WD[2] (youtube.com)

Megaminx = Ih Point Group: WE[2]

Megaminx = Ih Point Group: (21): WE[2] (youtube.com)

Megaminx = Ih Point Group: AB[2]

Megaminx = Ih Point Group: (22): AB[2] (youtube.com)

Megaminx = Ih Point Group: BC[2]

Megaminx = Ih Point Group: (23): BC[2] (youtube.com)

Megaminx = Ih Point Group: CD[2]

Megaminx = Ih Point Group: (24): CD[2] (youtube.com)

Megaminx = Ih Point Group: ED[2]

Megaminx = Ih Point Group: (25): ED[2] (youtube.com)

Megaminx = Ih Point Group: AE[2]

Megaminx = Ih Point Group: (26): AE[2] (youtube.com)

Megaminx = Ih Point Group: BG[2]

Megaminx = Ih Point Group: (27): BG[2] (youtube.com)

Megaminx = Ih Point Group: BF[2]

Megaminx = Ih Point Group: (28): BF[2] (youtube.com)

Megaminx = Ih Point Group: AF[2]

Megaminx = Ih Point Group: (29): AF[2] (youtube.com)

Megaminx = Ih Point Group: AN[2]

Megaminx = Ih Point Group: (30): AN[2] (youtube.com)

Megaminx = Ih Point Group: EN[2]

Megaminx = Ih Point Group: (31): EN[2] (youtube.com)

6S10:

Megaminx = Ih Point Group: SW[1/10]

Megaminx = Ih Point Group: (32): SW[1/10] (youtube.com)

Megaminx = Ih Point Group: SA[1/10]

Megaminx = Ih Point Group: (36): SA[1/10] (youtube.com)

Megaminx = Ih Point Group: SB[1/10]

The Math of the Rubik's Cube: Megaminx = Ih Point Group: (40): SB[1/10] (youtube.com)

Megaminx = Ih Point Group: SC[1/10] (To be published)

Megaminx = Ih Point Group: SD[1/10] (To be published)

Megaminx = Ih Point Group: SE[1/10] (To be published)

6S10^3:

Megaminx = Ih Point Group: SW[3/10]

Megaminx = Ih Point Group: (33): SW[3/10] (youtube.com)

Megaminx = Ih Point Group: SA[3/10]

Megaminx = Ih Point Group: (37): SA[3/10] (youtube.com)

Megaminx = Ih Point Group: SB[3/10] (To be published)

Megaminx = Ih Point Group: SC[3/10] (To be published)

Megaminx = Ih Point Group: SD[3/10] (To be published)

Megaminx = Ih Point Group: SE[3/10] (To be published)

6S10^7:

Megaminx = Ih Point Group: SW[7/10]

Megaminx = Ih Point Group: (34): SW[7/10] (youtube.com)

Megaminx = Ih Point Group: SA[7/10]

The Math of the Rubik's Cube: Megaminx = Ih Point Group: (38): SA[7/10] (youtube.com)

Megaminx = Ih Point Group: SB[7/10] (To be published)

Megaminx = Ih Point Group: SC[7/10] (To be published)

Megaminx = Ih Point Group: SD[7/10] (To be published)

Megaminx = Ih Point Group: SE[7/10] (To be published)

6S10^9:

Megaminx = Ih Point Group: SW[9/10]

Megaminx = Ih Point Group: (35): SW[9/10] (youtube.com)

Megaminx = Ih Point Group: SA[9/10]

The Math of the Rubik's Cube: Megaminx = Ih Point Group: (39): SA[9/10] (youtube.com)

Megaminx = Ih Point Group: SB[9/10] (To be published)

Megaminx = Ih Point Group: SC[9/10] (To be published)

Megaminx = Ih Point Group: SD[9/10] (To be published)

Megaminx = Ih Point Group: SE[9/10] (To be published)

10S6:

Megaminx = Ih Point Group: SWAB[1/6] (To be published)

Megaminx = Ih Point Group: SWBC[1/6] (To be published)

Megaminx = Ih Point Group: SWCD[1/6] (To be published)

Megaminx = Ih Point Group: SWDE[1/6] (To be published)

Megaminx = Ih Point Group: SWEA[1/6] (To be published)

Megaminx = Ih Point Group: SABF[1/6] (To be published)

Megaminx = Ih Point Group: SBCG[1/6] (To be published)

Megaminx = Ih Point Group: SCDH[1/6] (To be published)

Megaminx = Ih Point Group: SDEM[1/6] (To be published)

Megaminx = Ih Point Group: SEAN[1/6] (To be published)

10S6^5:

Megaminx = Ih Point Group: SWAB[5/6] (To be published)

Megaminx = Ih Point Group: SWBC[5/6] (To be published)

Megaminx = Ih Point Group: SWCD[5/6] (To be published)

Megaminx = Ih Point Group: SWDE[5/6] (To be published)

Megaminx = Ih Point Group: SWEA[5/6] (To be published)

Megaminx = Ih Point Group: SABF[5/6] (To be published)

Megaminx = Ih Point Group: SBCG[5/6] (To be published)

Megaminx = Ih Point Group: SCDH[5/6] (To be published)

Megaminx = Ih Point Group: SDEM[5/6] (To be published)

Megaminx = Ih Point Group: SEAN[5/6] (To be published)

15Q:

Megaminx = Ih Point Group: WA[m] (To be published)

Megaminx = Ih Point Group: WB[m] (To be published)

Megaminx = Ih Point Group: WC[m] (To be published)

Megaminx = Ih Point Group: WD[m] (To be published)

Megaminx = Ih Point Group: WE[m] (To be published)

Megaminx = Ih Point Group: AB[m] (To be published)

Megaminx = Ih Point Group: BC[m] (To be published)

Megaminx = Ih Point Group: CD[m] (To be published)

Megaminx = Ih Point Group: ED[m] (To be published)

Megaminx = Ih Point Group: AE[m] (To be published)

Megaminx = Ih Point Group: BG[m] (To be published)

Megaminx = Ih Point Group: BF[m] (To be published)

Megaminx = Ih Point Group: AF[m] (To be published)

Megaminx = Ih Point Group: AN[m] (To be published)

Megaminx = Ih Point Group: EN[m] (To be published)

i:

Megaminx = Ih Point Group: i (To be published)