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                                                                    EXHIBIT 4.12

                          CERTIFICATE OF INCORPORATION

                                       of

                                 FX Energy, Inc.

                     (Pursuant to Section 102 of the General
                    Corporation Law of the State of Delaware)

                                   ----------

        THE UNDERSIGNED, desiring to form a corporation pursuant to the
provisions of this General Corporation Law of the State of Delaware (hereinafter
referred to as the "GCL"), hereby certifies as follows:

        FIRST: The name of the corporation is FX Energy, Inc. (hereinafter
referred to as the "Company").

        SECOND: The address of the registered office of the Company in the State
of Delaware is 1013 Centre Road, City of Wilmington, County of New Castle,
Delaware 19805. The name of the registered agent of the Company at such address
is Corporation Service Company.

        THIRD: The nature of the business or purposes to be conducted or
promoted by the Company are:

        To engage in, promote, and carry on any lawful act or activity for which
        corporations may be organized under the GCL.

        FOURTH: The total number of shares of stock that the Company shall have
authority to issue is 1,000 shares of Common Stock, no par value per share.

        FIFTH: The name and mailing address of the sole incorporator of the
Company is David E. Alpine, c/o Whitman Breed Abbott & Morgan, 200 Park Avenue,
New York, New York 10166.

        SIXTH: The board of directors of the Company shall have the power to
adopt, amend or repeal the Bylaws of the Company at any meeting at which a
quorum is present by the affirmative vote of a majority of the whole board of
directors. Election of directors need not be by written ballot. Any director may
be removed at any time with or without cause, and the vacancy resulting from
such removal shall be filled, by vote of a majority of the stockholders of the
Company at a meeting called for that purpose or by unanimous consent in writing
of the stockholders.

        SEVENTH: To the fullest extent permitted by law, no director of the
Company shall be liable to the Company or its stockholders for monetary damages
for breach of fiduciary duty as a director.

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        THE UNDERSIGNED has executed this Certificate of Incorporation this 21st
day of February, 1996.


                                               /s/ David E. Alpine
                                               ---------------------------------
                                                   David E. Alpine
                                                   Sole Incorporator

                                       -2-

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                            CERTIFICATE OF AMENDMENT

                                       of

                          CERTIFICATE OF INCORPORATION

                                       of

                                 FX Energy, Inc.

                            (a Delaware corporation)

                         Pursuant to Section 242 of the

                       General Corporation Law of Delaware

                                   ----------

        The undersigned, desiring to amend the Certificate of Incorporation of
FX Energy, Inc. (hereinafter referred to as the "Company") under the provisions
of the General Corporation Law of the State of Delaware (hereinafter referred to
as the "GCL"), hereby certifies as follows:

        FIRST: Article "FIRST" of the Certificate of Incorporation of the
Company is hereby eliminated in its entirety and the following language is
substituted in lieu thereof:

        "FIRST": The name of the corporation is Cheniere Energy Operating Co.,
        Inc. (hereinafter referred to as the "Company")

        SECOND: The aforesaid amendment has been adopted, authorized and
declared advisable by (1) the unanimous written consent of the Board of
Directors of the Company under Section 141(f) of the GCL and (2) the unanimous
written consent of the stockholders of the Company under Section 228(a) of the
GCL, respectively, all in accordance with Section 242 of the GCL.

                                               FX ENERGY, INC.


                                               By:
                                                  ------------------------------
                                                  William D. Forster
                                                  President