Vary the application of the regulations herein established and establish appropriate requirements for irregular lots of less than the required area, existing in any district at the effective date of this chapter.

Vary the application of the regulations herein established and modify the requirements hereof in cases of exceptional topography under such conditions as will safeguard the neighborhood.

Grant temporary and conditional permits of limited duration for nonconforming uses and buildings in undeveloped sections.

Determine and establish the true location of district boundaries in any disputed case.

Where a zone boundary line divides a lot in single ownership at the effective date of this chapter, permit a use authorized on either portion of such lot to extend to the entire lot, but not more than 15 feet beyond the boundary line of the more restricted zone.

May permit the extension of a nonconforming use or building upon a lot occupied by such use or building, provided that the Board of Appeals determines that such use is reasonably consistent with the existing uses of other buildings, lots and premises in the neighboring territory in the Village, that the use will not unreasonably depreciate or impair the value of such other buildings, lots and premises in the neighboring territory and that such use will not present health, safety, traffic, nuisance or policing hazards which may not be adequately controlled.

May permit a public utility use in any district, provided that the Board of Appeals determines that the use is reasonably necessary for the health, safety, comfort or business purposes of the residents of the Village, that the use will not unreasonably depreciate or impair property values and that the use will not present health, safety, traffic, nuisance or policing hazards which may not be adequately controlled.

Determine whether or not any trade, industry, purpose or use otherwise permitted by this chapter would violate § 60-50 of Article VIII of this chapter and, if so, to prohibit such trade, industry or use.

Vary the height regulations in any district to permit church spires, belfries, towers, designed exclusively for ornamental purposes, flagstaffs, chimneys, flues or scenery lofts and to permit parapet walls extending not more than three feet above the height permitted by these regulations.

Permit any building, lot or premises in any district to be used as, by or for a college, a school other than a public school, a dormitory, a fraternity house, a recreation center, a philanthropic or eleemosynary institution, or a social center, except where the activities of any such use are those customarily carried on as a business, provided that the Board of Appeals determines that such use is reasonably consistent with existing uses in the neighboring territory, that the use will not unreasonably depreciate property values and that the use will not present health, safety, traffic, nuisance or policing hazards which may not be adequately controlled.

Not grant permits, as provided in Subsections F, G and J, except by unanimous vote of the Board of Appeals, if protests against the granting of any such permits are presented to the Board of Appeals before action on the application, signed by the owners of 25% of the frontage of land within 500 feet of the property in question, as shown by the last completed assessment roll of the Village.

After the Board of Appeals has granted a variance or other relief under the provisions of this chapter, such variance or other relief shall expire:

The Zoning Board of Appeals, for good cause shown, may extend the time in which to obtain a building permit, commence construction or complete construction, pursuant to the schedule set forth in this section, provided that such request for an extension of time is received by the Zoning Board of Appeals prior to the applicable expiration date and further provided that it finds that the conditions and circumstances essential to the original granting of the variance have not changed.

If any property owner has been granted a variance, but has not obtained a building permit as of the effective date of this section, the ninety-day period in which to obtain the building permit shall commence on the effective date of this section.